메뉴 건너뛰기




Volumn , Issue , 2006, Pages 1-312

Statistical mechanics of disordered systems: A mathematical perspective

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84925097065     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511616808     Document Type: Book
Times cited : (211)

References (263)
  • 1
    • 0034392041 scopus 로고    scopus 로고
    • On excursion sets, tube formulas and maxima of random fields
    • R. J. Adler. On excursion sets, tube formulas and maxima of random fields. Ann. Appl. Probab, 10(1):1–74, 2000.
    • (2000) Ann. Appl. Probab , vol.10 , Issue.1 , pp. 1-74
    • Adler, R.J.1
  • 2
    • 0002014946 scopus 로고
    • Translation invariance and instability of phase coexistence in the two dimensional using system
    • M. Aizenman. Translation invariance and instability of phase coexistence in the two dimensional using system. Comm. Math. Phys, 73(1):83–94, 1980.
    • (1980) Comm. Math. Phys , vol.73 , Issue.1 , pp. 83-94
    • Aizenman, M.1
  • 3
    • 0001937199 scopus 로고
    • The phase boundary in dilute and randomising and potts ferro magnets
    • M. Aizenman, J. T. Chayes, L. Chayes, and C. M. Newman. The phase boundary in dilute and randomising and Potts ferro magnets. J. Phys. A, 20(5):L313–18, 1987.
    • (1987) J. Phys. A , vol.20 , Issue.5 , pp. 313-318
    • Aizenman, M.1    Chayes, J.T.2    Chayes, L.3    Newman, C.M.4
  • 4
    • 0032165110 scopus 로고    scopus 로고
    • On the stability of the quenched state in mean-field spin-glass models
    • M. Aizenman and P. Contucci. On the stability of the quenched state in mean-field spin-glass models. J. Statist. Phys, 92(5–6):765–83, 1998.
    • (1998) J. Statist. Phys , vol.92 , Issue.5-6 , pp. 765-783
    • Aizenman, M.1    Contucci, P.2
  • 5
    • 0003124865 scopus 로고
    • Some rigorous results on the sherrington-kirkpatrick spin glass model
    • M. Aizenman, J. L. Lebowitz, and D. Ruelle. Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Comm. Math. Phys, 112(1):3–20, 1987.
    • (1987) Comm. Math. Phys , vol.112 , Issue.1 , pp. 3-20
    • Aizenman, M.1    Lebowitz, J.L.2    Ruelle, D.3
  • 6
    • 0000331178 scopus 로고
    • The third law of thermodynamics and the degeneracy of the ground state for lattice systems
    • M. Aizenman and E. H. Lieb. The third law of thermodynamics and the degeneracy of the ground state for lattice systems. J. Statist. Phys, 24(1):279–97, 1981.
    • (1981) J. Statist. Phys , vol.24 , Issue.1 , pp. 279-297
    • Aizenman, M.1    Lieb, E.H.2
  • 7
    • 1642452967 scopus 로고    scopus 로고
    • An extended variational principle for the sk spin-glass model
    • M. Aizenman, R. Sims, and S. L. Starr. An extended variational principle for the SK spin-glass model. Phys. Rev. B, 68(21):4403, 2003.
    • (2003) Phys. Rev. B , vol.68 , Issue.21 , pp. 4403
    • Aizenman, M.1    Sims, R.2    Starr, S.L.3
  • 8
    • 11744381258 scopus 로고
    • Rounding effects of quenched randomness on first-order phase transitions
    • M. Aizenman and J. Wehr. Rounding effects of quenched randomness on first-order phase transitions. Comm. Math. Phys, 130(3):489–528, 1990.
    • (1990) Comm. Math. Phys , vol.130 , Issue.3 , pp. 489-528
    • Aizenman, M.1    Wehr, J.2
  • 9
    • 33645063980 scopus 로고
    • Statistical mechanics of neural networks near saturation
    • D. J. Amit, H. Gutfreund, and H. Sompolinsky. Statistical mechanics of neural networks near saturation. Ann. Phys, 173:30–67, 1987.
    • (1987) Ann. Phys , vol.173 , pp. 30-67
    • Amit, D.J.1    Gutfreund, H.2    Sompolinsky, H.3
  • 10
    • 34547484735 scopus 로고
    • Theory of spin glasses
    • Ph. W. Anderson and S. F. Edwards. Theory of spin glasses. J. Phys. F, 5:965–74, 1975.
    • (1975) J. Phys. F , vol.5 , pp. 965-974
    • Anderson, P.H.1    Edwards, S.F.2
  • 12
    • 0040119868 scopus 로고
    • Ground state degeneracy and ferromagnetism in a spin glass
    • J. E. Avron, G. Roepstorff, and L. S. Schulman. Ground state degeneracy and ferromagnetism in a spin glass. J. Statist. Phys, 26(1):25–36, 1981.
    • (1981) J. Statist. Phys , vol.26 , Issue.1 , pp. 25-36
    • Avron, J.E.1    Roepstorff, G.2    Schulman, L.S.3
  • 13
    • 0034381954 scopus 로고    scopus 로고
    • Correlation a symptotics of classical lattice spin systems with nonconvex hamilton function at low temperature
    • V. Bach, T. Jecko, and J. Sjostrand. Correlation a symptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature. Ann. Henri Poincar´e, 1(1):59–100, 2000.
    • (2000) Ann. Henri Poincar´e , vol.1 , Issue.1 , pp. 59-100
    • Bach, V.1    Jecko, T.2    Sjostrand, J.3
  • 14
    • 80053975441 scopus 로고
    • Uniqueness of a gibbs field with a random potential – an elementary approach
    • L. A. Bassalygo and R. L. Dobrushin. Uniqueness of a Gibbs field with a random potential – an elementary approach. Teor. Veroyatnost. i Primenen, 31(4):651–70, 1986.
    • (1986) Teor. Veroyatnost. I Primenen , vol.31 , Issue.4 , pp. 651-670
    • Bassalygo, L.A.1    Dobrushin, R.L.2
  • 15
    • 0001938617 scopus 로고
    • A new combinatoric estimate for cluster expansions
    • G. A. Battle. A new combinatoric estimate for cluster expansions. Comm. Math. Phys, 94(1):133–9, 1984.
    • (1984) Comm. Math. Phys , vol.94 , Issue.1 , pp. 133-139
    • Battle, G.A.1
  • 16
    • 0003008062 scopus 로고
    • A note on cluster expansions, tree graph identities
    • G. A. Battle and P. Federbush. A note on cluster expansions, tree graph identities, extra 1/N! factors! Lett. Math. Phys, 8(1):55–7, 1984.
    • (1984) Lett. Math. Phys , vol.8 , Issue.1 , pp. 55-57
    • Battle, G.A.1    Federbush, P.2
  • 17
    • 34250251686 scopus 로고
    • The fkg inequality for the yukawa quantum field theory
    • G. A. Battle and L. Rosen. The FKG inequality for the Yukawa2 quantum field theory. J. Statist. Phys, 22(2):123–92, 1980.
    • (1980) J. Statist. Phys , vol.22 , Issue.2 , pp. 123-192
    • Battle, G.A.1    Rosen, L.2
  • 19
    • 42749098782 scopus 로고    scopus 로고
    • Universality in the level statistics of disordered systems
    • H. Bauke and St. Mertens. Universality in the level statistics of disordered systems. Phys. Rev. E, 70:025102(R), 2004.
    • (2004) Phys. Rev. E , pp. 70
    • Bauke, H.1    Mertens, S.T.2
  • 20
    • 0000632786 scopus 로고
    • Eight-vertex model in lattice statistics
    • R. J. Baxter. Eight-vertex model in lattice statistics. Phys. Rev. Lett, 26(14):832–3, 1971.
    • (1971) Phys. Rev. Lett , vol.26 , Issue.14 , pp. 832-833
    • Baxter, R.J.1
  • 21
    • 0004249508 scopus 로고
    • Amsterdam: North-Holland Publishing Co
    • C. Berge. Graphs and Hypergraphs. Amsterdam: North-Holland Publishing Co, 1973.
    • (1973) Graphs and Hypergraphs
    • Berge, C.1
  • 22
    • 34250109706 scopus 로고
    • Some properties of randomising models
    • A. Berretti. Some properties of randomising models. J. Statist. Phys, 38(3–4):483–96, 1985.
    • (1985) J. Statist. Phys , vol.38 , Issue.34 , pp. 483-496
    • Berretti, A.1
  • 23
    • 0035621332 scopus 로고    scopus 로고
    • Homogeneous fragmentation processes
    • J. Bertoin. Homogeneous fragmentation processes. Probab. Theory RelatedFields, 121(3):301–18, 2001.
    • (2001) Probab. Theory Relatedfields , vol.121 , Issue.3 , pp. 301-318
    • Bertoin, J.1
  • 25
    • 0034396569 scopus 로고    scopus 로고
    • The bolthausen–sznitman coalescent and the genealogy of continuous-state branching processes
    • J. Bertoin and J.-F. Le Gall. The Bolthausen–Sznitman coalescent and the genealogy of continuous-state branching processes. Probab. Theory Related Fields, 117(2):249–66, 2000.
    • (2000) Probab. Theory Related Fields , vol.117 , Issue.2 , pp. 249-266
    • Bertoin, J.1    Le Gall, J.-F.2
  • 26
    • 3042526534 scopus 로고    scopus 로고
    • Two coalescents derived from the ranges of stable subordinators
    • J. Bertoin and J. Pitman. Two coalescents derived from the ranges of stable subordinators. Electron. J. Probab, 5:no. 7, p. 17, 2000.
    • (2000) Electron. J. Probab , vol.5 , Issue.7 , pp. 17
    • Bertoin, J.1    Pitman, J.2
  • 27
    • 0037982096 scopus 로고    scopus 로고
    • On subordinators, self-similar markov processes and some factorizations of the exponential variable
    • J. Bertoin and M. Yor. On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Electron. Comm. Probab, 6:95–106 (electronic), 2001.
    • (2001) Electron. Comm. Probab , vol.6 , pp. 95-106
    • Bertoin, J.1    Yor, M.2
  • 29
    • 0030493568 scopus 로고    scopus 로고
    • One-dimensional random-field using model: Gibbs states and structure of ground states
    • P. M. Bleher, J. Ruiz, and V. A. Zagrebnov. One-dimensional random-field Using model: Gibbs states and structure of ground states. J. Statist. Phys, 84(5–6):1077–93, 1996.
    • (1996) J. Statist. Phys , vol.84 , Issue.5-6 , pp. 1077-1093
    • Bleher, P.M.1    Ruiz, J.2    Zagrebnov, V.A.3
  • 30
    • 33645132488 scopus 로고    scopus 로고
    • Translation invariant gibbs states for the using model
    • T. Bodineau. Translation invariant Gibbs states for the using model. Probab. Theory Related Fields (online) DOI 10.1007/s00440–005–0457–0, 2005.
    • (2005) Probab. Theory Related Fields
    • Bodineau, T.1
  • 31
    • 0034345434 scopus 로고    scopus 로고
    • Rigorous probabilistic analysis of equilibrium crystal shapes
    • T. Bodineau, D. Ioffe, and Y. Velenik. Rigorous probabilistic analysis of equilibrium crystal shapes. J. Math. Phys, 41(3):1033–98, 2000.
    • (2000) J. Math. Phys , vol.41 , Issue.3 , pp. 1033-1098
    • Bodineau, T.1    Ioffe, D.2    Velenik, Y.3
  • 33
    • 0010117449 scopus 로고    scopus 로고
    • On ruelle's probability cascades and an abstract cavity method
    • E. Bolthausen and A.-S. Sznitman. On Ruelle's probability cascades and an abstract cavity method. Comm. Math. Phys, 197(2):247–76, 1998.
    • (1998) Comm. Math. Phys , vol.197 , Issue.2 , pp. 247-276
    • Bolthausen, E.1    Sznitman, A.-S.2
  • 34
    • 0042909128 scopus 로고    scopus 로고
    • Ten lectures on random media
    • Basel: Birkh¨auser Verlag
    • E. Bolthausen and A.-S. Sznitman. Ten Lectures on Random Media, vol. 32 of DMV Seminar. Basel: Birkh¨auser Verlag, 2002.
    • (2002) DMV Seminar , vol.32
    • Bolthausen, E.1    Sznitman, A.-S.2
  • 35
    • 0035539876 scopus 로고    scopus 로고
    • Phase transition and finite-size scaling for the integer partitioning problem
    • C. Borgs, J. Chayes, and B. Pittel. Phase transition and finite-size scaling for the integer partitioning problem. Random Structures Algorithms, 19(3–4):247–88, 2001.
    • (2001) Random Structures Algorithms , vol.19 , Issue.3-4 , pp. 247-288
    • Borgs, C.1    Chayes, J.2    Pittel, B.3
  • 36
    • 11144303514 scopus 로고    scopus 로고
    • Phase diagram for the constrained integer partitioning problem
    • C. Borgs, J. T. Chayes, S. Mertens, and B. Pittel. Phase diagram for the constrained integer partitioning problem. Random Structures Algorithms, 24(3):315–80, 2004.
    • (2004) Random Structures Algorithms , vol.24 , Issue.3 , pp. 315-380
    • Borgs, C.1    Chayes, J.T.2    Mertens, S.3    Pittel, B.4
  • 37
    • 0032049568 scopus 로고    scopus 로고
    • The kac version of the sherrington–kirkpatrick model at high temperatures
    • A. Bovier. The Kac version of the Sherrington–Kirkpatrick model at high temperatures. J. Statist. Phys, 91(1–2):459–74, 1998.
    • (1998) J. Statist. Phys , vol.91 , Issue.1-2 , pp. 459-474
    • Bovier, A.1
  • 38
    • 0010294155 scopus 로고    scopus 로고
    • Statistical mechanics of disordered systems
    • Aarhus University
    • A. Bovier. Statistical Mechanics of Disordered Systems, vol. 10 of Ma PhySto Lecture Notes. Aarhus University, 2001.
    • (2001) Ma Physto Lecture Notes , vol.10
    • Bovier, A.1
  • 39
    • 0041051865 scopus 로고    scopus 로고
    • An almost sure central limit theorem for the hopfield model
    • A. Bovier and V. Gayrard. An almost sure central limit theorem for the Hopfield model. Markov Process. Related Fields, 3(2):151–73, 1997.
    • (1997) Markov Process. Related Fields , vol.3 , Issue.2 , pp. 151-173
    • Bovier, A.1    Gayrard, V.2
  • 40
    • 0030673431 scopus 로고    scopus 로고
    • The retrieval phase of the hopfield model: A rigorous analysis of the overlap distribution
    • A. Bovier and V. Gayrard. The retrieval phase of the Hopfield model: a rigorous analysis of the overlap distribution. Probab. Theory Related Fields, 107(1):61–98, 1997.
    • (1997) Probab. Theory Related Fields , vol.107 , Issue.1 , pp. 61-98
    • Bovier, A.1    Gayrard, V.2
  • 41
    • 0004340648 scopus 로고    scopus 로고
    • Hopfield models as generalized random mean field models
    • Boston, MA: Birkh¨auser Boston
    • A. Bovier and V. Gayrard. Hopfield models as generalized random mean field models. In Mathematical Aspects of Spin Glasses and Neural Networks, vol. 41 of Progr. Probab, pp. 3–89. Boston, MA: Birkh¨auser Boston, 1998.
    • (1998) Mathematical Aspects of Spin Glasses and Neural Networks , vol.41 , pp. 3-89
    • Bovier, A.1    Gayrard, V.2
  • 42
    • 0009160041 scopus 로고    scopus 로고
    • Metastates in the hopfield model in the replica symmetric regime
    • A. Bovier and V. Gayrard. Metastates in the Hopfield model in the replica symmetric regime. Math. Phys. Anal. Geom, 1(2):107–44, 1998.
    • (1998) Math. Phys. Anal. Geom , vol.1 , Issue.2 , pp. 107-144
    • Bovier, A.1    Gayrard, V.2
  • 43
    • 21844481797 scopus 로고
    • Gibbs states of the hopfield model in the regime of perfect memory
    • A. Bovier, V. Gayrard, and P. Picco. Gibbs states of the Hopfield model in the regime of perfect memory. Probab. Theory Related Fields, 100(3):329–63, 1994.
    • (1994) Probab. Theory Related Fields , vol.100 , Issue.3 , pp. 329-363
    • Bovier, A.1    Gayrard, V.2    Picco, P.3
  • 44
    • 21844510860 scopus 로고
    • Gibbs states of the hopfield model with extensively many patterns
    • A. Bovier, V. Gayrard, and P. Picco. Gibbs states of the Hopfield model with extensively many patterns. J. Statist. Phys, 79(1–2):395–414, 1995.
    • (1995) J. Statist. Phys , vol.79 , Issue.1-2 , pp. 395-414
    • Bovier, A.1    Gayrard, V.2    Picco, P.3
  • 45
    • 21844511557 scopus 로고
    • Large deviation principles for the hopfield model and the kac-hopfield model
    • A. Bovier, V. Gayrard, and P. Picco. Large deviation principles for the Hopfield model and the Kac-Hopfield model. Probab. Theory Related Fields, 101(4):511–46, 1995.
    • (1995) Probab. Theory Related Fields , vol.101 , Issue.4 , pp. 511-546
    • Bovier, A.1    Gayrard, V.2    Picco, P.3
  • 46
    • 0039260327 scopus 로고    scopus 로고
    • Distribution of overlap profiles in the one-dimensional kac–hopfield model
    • A. Bovier, V. Gayrard, and P. Picco. Distribution of overlap profiles in the one-dimensional Kac–Hopfield model. Comm. Math. Phys, 186(2):323–79, 1997.
    • (1997) Comm. Math. Phys , vol.186 , Issue.2 , pp. 323-379
    • Bovier, A.1    Gayrard, V.2    Picco, P.3
  • 47
    • 34249841562 scopus 로고
    • Stability of hierarchical interfaces in a random field model
    • A. Bovier and C. Kulske. Stability of hierarchical interfaces in a random field model. J. Statist. Phys, 69(1–2):79–110, 1992.
    • (1992) J. Statist. Phys , vol.69 , Issue.1-2 , pp. 79-110
    • Bovier, A.1    Kulske, C.2
  • 48
    • 34250080732 scopus 로고
    • Hierarchical interfaces in random media. Ii. The gibbs measures
    • A. Bovier and C. Kulske. Hierarchical interfaces in random media. II. The Gibbs measures. J. Statist. Phys, 73(1–2):253–66, 1993.
    • (1993) J. Statist. Phys , vol.73 , Issue.1-2 , pp. 253-266
    • Bovier, A.1    Kulske, C.2
  • 49
    • 0000178537 scopus 로고
    • A rigorous renormalization group method for interfaces in random media
    • A. Bovier and C. Kulske. A rigorous renormalization group method for interfaces in random media. Rev. Math. Phys, 6(3):413–96, 1994.
    • (1994) Rev. Math. Phys , vol.6 , Issue.3 , pp. 413-496
    • Bovier, A.1    Kulske, C.2
  • 50
    • 85066683333 scopus 로고    scopus 로고
    • Gibbs measures of derrida's generalized random energy models and genealogies of neveu's continuous state branching processe
    • A. Bovier and I. Kurkova. Gibbs measures of Derrida's generalized random energy models and genealogies of Neveu's continuous state branching processe. Preprint 854, WIAS, 2003.
    • (2003) WIAS
    • Bovier, A.1    Kurkova, I.2
  • 51
    • 2942556515 scopus 로고    scopus 로고
    • Derrida's generalised random energy models. I. Models with finitely many hierarchies
    • A. Bovier and I. Kurkova. Derrida's generalised random energy models. I. Models with finitely many hierarchies. Ann. Inst. H. Poincar´e Probab. Statist, 40(4):439–80, 2004.
    • (2004) Ann. Inst. H. Poincar´e Probab. Statist , vol.40 , Issue.4 , pp. 439-480
    • Bovier, A.1    Kurkova, I.2
  • 52
    • 2942560194 scopus 로고    scopus 로고
    • Derrida's generalized random energy models. Ii. Models with continuous hierarchies
    • A. Bovier and I. Kurkova. Derrida's generalized random energy models. II. Models with continuous hierarchies. Ann. Inst. H. Poincar´e Probab. Statist, 40(4):481–95, 2004.
    • (2004) Ann. Inst. H. Poincar´e Probab. Statist , vol.40 , Issue.4 , pp. 481-495
    • Bovier, A.1    Kurkova, I.2
  • 53
    • 85066653662 scopus 로고    scopus 로고
    • Poisson convergence in the restricted k-partioning problem
    • A. Bovier and I. Kurkova. Poisson convergence in the restricted k-partioning problem. Preprint 964, WIAS, 2004.
    • (2004) WIAS
    • Bovier, A.1    Kurkova, I.2
  • 54
    • 85066722397 scopus 로고    scopus 로고
    • Level statistics of disordered systems: A proof of the local rem conjecture
    • A. Bovier and I. Kurkova. Level statistics of disordered systems: a proof of the local REM conjecture. Preprint 1023, WIAS, 2005.
    • (2005) WIAS
    • Bovier, A.1    Kurkova, I.2
  • 55
    • 0036018190 scopus 로고    scopus 로고
    • Fluctuations of the free energy in the rem and the p-spin sk models
    • A. Bovier, I. Kurkova, and M. Lowe. Fluctuations of the free energy in the REM and the p-spin SK models. Ann. Probab, 30(2):605–51, 2002.
    • (2002) Ann. Probab , vol.30 , Issue.2 , pp. 605-651
    • Bovier, A.1    Kurkova, I.2    Lowe, M.3
  • 56
    • 0035626683 scopus 로고    scopus 로고
    • Extreme value behavior in the hopfield model
    • A. Bovier and D. M. Mason. Extreme value behavior in the Hopfield model. Ann. Appl. Probab, 11(1):91–120, 2001.
    • (2001) Ann. Appl. Probab , vol.11 , Issue.1 , pp. 91-120
    • Bovier, A.1    Mason, D.M.2
  • 57
    • 58149230264 scopus 로고    scopus 로고
    • The spin-glass phase-transition in the hopfield model with p-spin interactions
    • A. Bovier and B. Niederhauser. The spin-glass phase-transition in the Hopfield model with p-spin interactions. Adv. Theor. Math. Phys, 5(6):1001–46, 2001.
    • (2001) Adv. Theor. Math. Phys , vol.5 , Issue.6 , pp. 1001-1046
    • Bovier, A.1    Niederhauser, B.2
  • 58
    • 34249924878 scopus 로고
    • Stability of interfaces in a random environment. A rigorous renormalization group analysis of a hierarchical model
    • A. Bovier and P. Picco. Stability of interfaces in a random environment. A rigorous renormalization group analysis of a hierarchical model. J. Statist. Phys, 62(1–2):177–99, 1991.
    • (1991) J. Statist. Phys , vol.62 , Issue.1-2 , pp. 177-199
    • Bovier, A.1    Picco, P.2
  • 59
    • 0033246855 scopus 로고    scopus 로고
    • Stochastic symmetry-breaking in a gaussian hopfield model
    • A. Bovier, A. C. D. van Enter, and B. Niederhauser. Stochastic symmetry-breaking in a Gaussian Hopfield model. J. Statist. Phys, 95(1–2):181–213, 1999.
    • (1999) J. Statist. Phys , vol.95 , Issue.1-2 , pp. 181-213
    • Bovier, A.1    Van Enter, A.C.2    Niederhauser, B.3
  • 60
    • 0034338443 scopus 로고    scopus 로고
    • A simple inductive approach to the problem of convergence of cluster expansions of polymer models
    • A. Bovier and M. Zahradnýk. A simple inductive approach to the problem of convergence of cluster expansions of polymer models. J. Statist. Phys, 100(3–4):765–78, 2000.
    • (2000) J. Statist. Phys , vol.100 , Issue.3-4 , pp. 765-778
    • Bovier, A.1    Zahradnýk, M.2
  • 61
    • 49549132663 scopus 로고
    • On extensions of the brunn–minkowski and pr´ekopa–leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
    • H. J. Brascamp and E. H. Lieb. On extensions of the Brunn–Minkowski and Pr´ekopa–Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. J. Functional Analysis, 22(4):366–89, 1976.
    • (1976) J. Functional Analysis , vol.22 , Issue.4 , pp. 366-389
    • Brascamp, H.J.1    Lieb, E.H.2
  • 62
    • 0000702675 scopus 로고
    • Phase transition in the 3d random field using model
    • J. Bricmont and A. Kupiainen. Phase transition in the 3d random field using model. Comm. Math. Phys, 116(4):539–72, 1988.
    • (1988) Comm. Math. Phys , vol.116 , Issue.4 , pp. 539-572
    • Bricmont, J.1    Kupiainen, A.2
  • 63
    • 0002453502 scopus 로고
    • Phase transitions in systems with a finite number of dominant ground states
    • J. Bricmont and J. Slawny. Phase transitions in systems with a finite number of dominant ground states. J. Statist. Phys, 54(1–2):89–161, 1989.
    • (1989) J. Statist. Phys , vol.54 , Issue.1-2 , pp. 89-161
    • Bricmont, J.1    Slawny, J.2
  • 64
    • 0000708826 scopus 로고
    • A new form of the mayer expansion in classical statistical mechanics
    • D. Brydges and P. Federbush. A new form of the Mayer expansion in classical statistical mechanics. J. Math. Phys, 19(10):2064–7, 1978.
    • (1978) J. Math. Phys , vol.19 , Issue.10 , pp. 2064-2067
    • Brydges, D.1    Federbush, P.2
  • 65
    • 1442357094 scopus 로고    scopus 로고
    • Branched polymers and dimensional reduction
    • D. C. Brydges and J. Z. Imbrie. Branched polymers and dimensional reduction. Ann. of Math. (2), 158(3):1019–39, 2003.
    • (2003) Ann. Of Math , vol.158 , Issue.3 , pp. 1019-1039
    • Brydges, D.C.1    Imbrie, J.Z.2
  • 67
    • 0000182012 scopus 로고
    • The fundamental theorem of the theory of scattering billiards
    • L. A. Bunimovic and J. G. Sinai. The fundamental theorem of the theory of scattering billiards. Mat. Sb. (N.S.), 90(132):415–31, 1973.
    • (1973) Mat. Sb , vol.90 , Issue.132 , pp. 415-431
    • Bunimovic, L.A.1    Sinai, J.G.2
  • 69
    • 0001042417 scopus 로고
    • Decay of correlations for infinite range interactions in unbounded spin systems
    • C. Cammarota. Decay of correlations for infinite range interactions in unbounded spin systems. Comm. Math. Phys, 85(4):517–28, 1982.
    • (1982) Comm. Math. Phys , vol.85 , Issue.4 , pp. 517-528
    • Cammarota, C.1
  • 70
    • 0011409893 scopus 로고
    • On the existence of thermodynamics for the generalized random energy model
    • D. Capocaccia, M. Cassandro, and P. Picco. On the existence of thermodynamics for the generalized random energy model. J. Statist. Phys, 46(3-4):493-505, 1987.
    • (1987) J. Statist. Phys , vol.46 , Issue.3-4 , pp. 493-505
    • Capocaccia, D.1    Cassandro, M.2    Picco, P.3
  • 72
    • 0033164052 scopus 로고    scopus 로고
    • Typical configurations for one-dimensional random field kac model
    • M. Cassandro, E. Orlandi, and P. Picco. Typical configurations for one-dimensional random field Kac model. Ann. Probab, 27(3):1414–1467, 1999.
    • (1999) Ann. Probab , vol.27 , Issue.3 , pp. 1414-1467
    • Cassandro, M.1    Orlandi, E.2    Picco, P.3
  • 73
    • 23244433756 scopus 로고    scopus 로고
    • One-dimensional random field kac's model: Localization of the phases
    • M. Cassandro, E. Orlandi, P. Picco, and M. E. Vares. One-dimensional random field Kac's model: localization of the phases. Electronic J. Probab, 10:786–864, 2005.
    • (2005) Electronic J. Probab , vol.10 , pp. 786-864
    • Cassandro, M.1    Orlandi, E.2    Picco, P.3    Vares, M.E.4
  • 74
    • 0034563464 scopus 로고    scopus 로고
    • Large deviations of the finite cluster shape for two-dimensional percolation in the hausdorff and l1 metric
    • R. Cerf. Large deviations of the finite cluster shape for two-dimensional percolation in the Hausdorff and L1 metric. J. Theoret. Probab, 13(2):491–517, 2000.
    • (2000) J. Theoret. Probab , vol.13 , Issue.2 , pp. 491-517
    • Cerf, R.1
  • 75
    • 0042238349 scopus 로고    scopus 로고
    • Phase coexistence in ising, potts and percolation models
    • R. Cerf and A. Pisztora. Phase coexistence in Ising, Potts and percolation models. Ann. Inst. H. Poincar´e Probab. Statist, 37(6):643–724, 2001.
    • (2001) Ann. Inst. H. Poincar´e Probab. Statist , vol.37 , Issue.6 , pp. 643-724
    • Cerf, R.1    Pisztora, A.2
  • 76
    • 0009228176 scopus 로고
    • On the lower critical dimensionality of the using model in a random field
    • J. T. Chalker. On the lower critical dimensionality of the Using model in a random field. J. Phys. C, 16:6615–22, 1983.
    • (1983) J. Phys. C , vol.16 , pp. 6615-6622
    • Chalker, J.T.1
  • 78
    • 0001678444 scopus 로고
    • Large deviation estimates for a conditional probability distribution. Applications to random interaction gibbs measures
    • F. Comets. Large deviation estimates for a conditional probability distribution. Applications to random interaction Gibbs measures. Probab. Theory Related Fields, 80(3):407–32, 1989.
    • (1989) Probab. Theory Related Fields , vol.80 , Issue.3 , pp. 407-432
    • Comets, F.1
  • 79
    • 23044530670 scopus 로고    scopus 로고
    • Ordered overlaps in disordered mean-field models
    • F. Comets and A. Dembo. Ordered overlaps in disordered mean-field models. Probab. Theory Related Fields, 121(1):1–29, 2001.
    • (2001) Probab. Theory Related Fields , vol.121 , Issue.1 , pp. 1-29
    • Comets, F.1    Dembo, A.2
  • 80
    • 34249756647 scopus 로고
    • The sherrington–kirkpatrick model of spin glasses and stochastic calculus: The high temperature case
    • F. Comets and J. Neveu. The Sherrington–Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case. Comm. Math. Phys, 166(3):549–64, 1995.
    • (1995) Comm. Math. Phys , vol.166 , Issue.3 , pp. 549-564
    • Comets, F.1    Neveu, J.2
  • 81
    • 0038468718 scopus 로고    scopus 로고
    • Thermo dynamical limit for correlated gaussian random energy models
    • P. Contucci, M. Degli Esposti, C. Giardina, and S. Graffi. Thermo dynamical limit for correlated Gaussian random energy models. Comm. Math. Phys, 236(1):55–63, 2003.
    • (2003) Comm. Math. Phys , vol.236 , Issue.1 , pp. 55-63
    • Contucci, P.1    Degli Esposti, M.2    Giardina, C.3    Graffi, S.4
  • 82
    • 10344247177 scopus 로고    scopus 로고
    • Random multi-overlap structures and cavity fields in diluted spin glasses
    • L. De Sanctis. Random multi-overlap structures and cavity fields in diluted spin glasses. J. Statist. Phys, 117:785–99, 2005.
    • (2005) J. Statist. Phys , vol.117 , pp. 785-799
    • De Sanctis, L.1
  • 83
    • 0042521830 scopus 로고
    • Inequalities of fkg type
    • W. F. den Hollander and M. Keane. Inequalities of FKG type. Physica, 138A:167–82, 1986.
    • (1986) Physica , vol.138 , pp. 167-182
    • Den Hollander, W.F.1    Keane, M.2
  • 84
    • 35949021286 scopus 로고
    • Random-energy model: Limit of a family of disordered models
    • B. Derrida. Random-energy model: limit of a family of disordered models. Phys. Rev. Lett, 45(2):79–82, 1980.
    • (1980) Phys. Rev. Lett , vol.45 , Issue.2 , pp. 79-82
    • Derrida, B.1
  • 85
    • 4243861085 scopus 로고
    • Random-energy model: An exactly solvable model of disordered systems
    • B. Derrida. Random-energy model: an exactly solvable model of disordered systems. Phys. Rev. B (3), 24(5):2613–26, 1981.
    • (1981) Phys. Rev. B , vol.24 , Issue.5 , pp. 2613-2626
    • Derrida, B.1
  • 86
    • 0000843415 scopus 로고
    • A generalisation of the random energy model that includes correlations between the energies
    • B. Derrida. A generalisation of the random energy model that includes correlations between the energies. J. Phys. Lett, 46:401–7, 1985.
    • (1985) J. Phys. Lett , vol.46 , pp. 401-407
    • Derrida, B.1
  • 88
    • 0039172260 scopus 로고
    • Existence of a phase transition in the two-dimensional and three-dimensional using models
    • R. L. Dobrushin. Existence of a phase transition in the two-dimensional and three-dimensional Using models. Soviet Physics Dokl, 10:111–13, 1965.
    • (1965) Soviet Physics Dokl , vol.10 , pp. 111-113
    • Dobrushin, R.L.1
  • 89
    • 0001722765 scopus 로고
    • Gibbs states that describe coexistence of phases for a three-dimensional using model
    • R. L. Dobrushin. Gibbs states that describe coexistence of phases for a three-dimensional Using model. Theor. Probab. Appl, 17:582–600, 1972.
    • (1972) Theor. Probab. Appl , vol.17 , pp. 582-600
    • Dobrushin, R.L.1
  • 90
    • 0002173067 scopus 로고    scopus 로고
    • Estimates of semi-invariants for the using model at low temperatures
    • Providence, RI: American Mathematical Society
    • R. L. Dobrushin. Estimates of semi-invariants for the using model at low temperatures. In Topics in Statistical and Theoretical Physics, vol. 177 of Amer. Math. Soc. Transl. Ser. 2, pp. 59–81. Providence, RI: American Mathematical Society, 1996.
    • (1996) Topics in Statistical and Theoretical Physics , vol.177 , pp. 59-81
    • Dobrushin, R.L.1
  • 91
    • 0033466556 scopus 로고    scopus 로고
    • Non-gibbsian states and their gibbs description
    • R. L. Dobrushin and S. B. Shlosman. ‘Non-Gibbsian’ states and their Gibbs description. Comm. Math. Phys, 200(1):125–79, 1999.
    • (1999) Comm. Math. Phys , vol.200 , Issue.1 , pp. 125-179
    • Dobrushin, R.L.1    Shlosman, S.B.2
  • 92
    • 0001235413 scopus 로고
    • Description of a random field by means of conditional probabilities and conditions for its regularity
    • R. L. Dobrusin. Description of a random field by means of conditional probabilities and conditions for its regularity. Teor. Verojatnost. i Primenen, 13:201–29, 1968.
    • (1968) Teor. Verojatnost. I Primenen , vol.13 , pp. 201-229
    • Dobrusin, R.L.1
  • 93
    • 0000080779 scopus 로고
    • Definition of a system of random variables by means of conditional distributions
    • R. L. Dobrusin. Definition of a system of random variables by means of conditional distributions. Teor. Verojatnost. i Primenen, 15:469–97, 1970.
    • (1970) Teor. Verojatnost. I Primenen , vol.15 , pp. 469-497
    • Dobrusin, R.L.1
  • 94
    • 0035095833 scopus 로고    scopus 로고
    • Large deviations and the random energy model
    • T. C. Dorlas and J. R. Wedagedera. Large deviations and the random energy model. Internat. J. Modern Phys. B, 15(1):1–15, 2001.
    • (2001) Internat J. Modern Phys. B , vol.15 , Issue.1 , pp. 1-15
    • Dorlas, T.C.1    Wedagedera, J.R.2
  • 96
    • 0001588819 scopus 로고
    • On a third-order phase transition
    • T. Eisele. On a third-order phase transition. Comm. Math. Phys, 90(1):125–59, 1983.
    • (1983) Comm. Math. Phys , vol.90 , Issue.1 , pp. 125-159
    • Eisele, T.1
  • 97
    • 0004100744 scopus 로고
    • Entropy, large deviations, and statistical mechanics
    • New York: Springer-Verlag
    • R. S. Ellis. Entropy, Large Deviations, and Statistical Mechanics, vol. 271 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. New York: Springer-Verlag, 1985.
    • (1985) Grundlehren Der Mathematischen Wissenschaften , vol.271
    • Ellis, R.S.1
  • 98
    • 36749114080 scopus 로고
    • The semi-euclidean approach in statistical mechanics. Ii. The cluster expansion, a special example
    • P. Federbush. The semi-Euclidean approach in statistical mechanics. II. The cluster expansion, a special example. J. Mathematical Phys, 17(2):204–7, 1976.
    • (1976) J. Mathematical Phys , vol.17 , Issue.2 , pp. 204-207
    • Federbush, P.1
  • 99
    • 22244444842 scopus 로고
    • Absence of many states in realistic spin glasses
    • D. S. Fisher and D. A. Huse. Absence of many states in realistic spin glasses. J. Phys. A, 20(15):1005–10, 1987.
    • (1987) J. Phys. A , vol.20 , Issue.15 , pp. 1005-1010
    • Fisher, D.S.1    Huse, D.A.2
  • 100
    • 0009229280 scopus 로고
    • The using model in a random magnetic field
    • D. S. Fisher, J. Frohlich, and T. Spencer. The Using model in a random magnetic field. J. Statist. Phys, 34(5–6):863–70, 1984.
    • (1984) J. Statist. Phys , vol.34 , Issue.5-6 , pp. 863-870
    • Fisher, D.S.1    Frohlich, J.2    Spencer, T.3
  • 101
    • 0000962398 scopus 로고
    • The free energy of a macroscopic system
    • M. E. Fisher. The free energy of a macroscopic system. Arch. Rational Mech. Anal, 17:377–410, 1964.
    • (1964) Arch. Rational Mech. Anal , vol.17 , pp. 377-410
    • Fisher, M.E.1
  • 102
    • 0002748055 scopus 로고
    • Correlation inequalities on some partially ordered sets
    • C. M. Fortuin, P. W. Kasteleyn, and J. Ginibre. Correlation inequalities on some partially ordered sets. Comm. Math. Phys, 22:89–103, 1971.
    • (1971) Comm. Math. Phys , vol.22 , pp. 89-103
    • Fortuin, C.M.1    Kasteleyn, P.W.2    Ginibre, J.3
  • 103
    • 0242509834 scopus 로고    scopus 로고
    • Replica bounds for diluted non-poissonian spin systems
    • S. Franz, M. Leone, and F. L. Toninelli. Replica bounds for diluted non-Poissonian spin systems. J. Phys. A, 36(43):10967–85, 2003.
    • (2003) J. Phys. A , vol.36 , Issue.43 , pp. 10967-10985
    • Franz, S.1    Leone, M.2    Toninelli, F.L.3
  • 104
    • 3543019687 scopus 로고    scopus 로고
    • Finite range spin glasses in the kac limit: Free energy and local observables
    • S. Franz and F. L. Toninelli. Finite range spin glasses in the Kac limit: free energy and local observables. J. Phys. A, 37(30):7433–46, 2004.
    • (2004) J. Phys. A , vol.37 , Issue.30 , pp. 7433-7446
    • Franz, S.1    Toninelli, F.L.2
  • 105
    • 0040407132 scopus 로고
    • Improved perturbation expansion for disordered systems: Beating griffiths singularities
    • J. Frohlich and J. Z. Imbrie. Improved perturbation expansion for disordered systems: beating Griffiths singularities. Comm. Math. Phys, 96(2):145–80, 1984.
    • (1984) Comm. Math. Phys , vol.96 , Issue.2 , pp. 145-180
    • Frohlich, J.1    Imbrie, J.Z.2
  • 106
    • 0041001274 scopus 로고
    • The high-temperature phase of long-range spin glasses
    • J. Frohlich and B. Zegarlinski. The high-temperature phase of long-range spin glasses. Comm. Math. Phys, 110(1):121–55, 1987.
    • (1987) Comm. Math. Phys , vol.110 , Issue.1 , pp. 121-155
    • Frohlich, J.1    Zegarlinski, B.2
  • 107
    • 4243543378 scopus 로고
    • Spin glasses and other lattice systems with long range interactions
    • J. Frohlich and B. Zegarlinski. Spin glasses and other lattice systems with long range interactions. Comm. Math. Phys, 120(4):665–88, 1989.
    • (1989) Comm. Math. Phys , vol.120 , Issue.4 , pp. 665-688
    • Frohlich, J.1    Zegarlinski, B.2
  • 109
    • 0009151930 scopus 로고
    • Correlation functions of a lattice system
    • G. Gallavotti and S. Miracle-Sole. Correlation functions of a lattice system. Comm. Math. Phys, 7:274–88, 1968.
    • (1968) Comm. Math. Phys , vol.7 , pp. 274-288
    • Gallavotti, G.1    Miracle-Sole, S.2
  • 110
    • 0002160945 scopus 로고
    • Equilibrium states of the using model in the two-phase region
    • G. Gallavotti and S. Miracle-Sole. Equilibrium states of the Using model in the two-phase region. Phys. Rev, B5:2555–9, 1973.
    • (1973) Phys. Rev , vol.5 , pp. 2555-2559
    • Gallavotti, G.1    Miracle-Sole, S.2
  • 112
    • 0000518213 scopus 로고
    • Fluctuations in derrida's random energy and generalized random energy models
    • A. Galves, S. Martýnez, and P. Picco. Fluctuations in Derrida's random energy and generalized random energy models. J. Statist. Phys, 54(1–2):515–29, 1989.
    • (1989) J. Statist. Phys , vol.54 , Issue.1-2 , pp. 515-529
    • Galves, A.1    Martýnez, S.2    Picco, P.3
  • 113
    • 0000996412 scopus 로고
    • Magnetic properties and function q(X) of the generalised random energy model
    • E. Gardner and B. Derrida. Magnetic properties and function q(x) of the generalised random energy model. J. Phys. C, 19:5783–98, 1986.
    • (1986) J. Phys. C , vol.19 , pp. 5783-5798
    • Gardner, E.1    Derrida, B.2
  • 114
    • 20444430048 scopus 로고
    • Solution of the generalised random energy model
    • E. Gardner and B. Derrida. Solution of the generalised random energy model. J. Phys. C, 19:2253–74, 1986.
    • (1986) J. Phys. C , vol.19 , pp. 2253-2274
    • Gardner, E.1    Derrida, B.2
  • 115
    • 0003099623 scopus 로고
    • The probability distribution of the partition function of the random energy model
    • E. Gardner and B. Derrida. The probability distribution of the partition function of the random energy model. J. Phys. A, 22(12):1975–81, 1989.
    • (1989) J. Phys. A , vol.22 , Issue.12 , pp. 1975-1981
    • Gardner, E.1    Derrida, B.2
  • 116
    • 0038506585 scopus 로고
    • Thermodynamic limit of the q-state potts–hopfield model with infinitely many patterns
    • V. Gayrard. Thermodynamic limit of the q-state Potts–Hopfield model with infinitely many patterns. J. Statist. Phys, 68(5–6):977–1011, 1992.
    • (1992) J. Statist. Phys , vol.68 , Issue.5-6 , pp. 977-1011
    • Gayrard, V.1
  • 117
    • 0001436319 scopus 로고
    • A limit theorem for the norm of random matrices
    • S. Geman. A limit theorem for the norm of random matrices. Ann. Probab, 8(2):252–61, 1980.
    • (1980) Ann. Probab , vol.8 , Issue.2 , pp. 252-261
    • Geman, S.1
  • 118
    • 0030352771 scopus 로고    scopus 로고
    • A central limit theorem for the overlap in the hopfield model
    • B. Gentz. A central limit theorem for the overlap in the Hopfield model. Ann. Probab, 24(4):1809–41, 1996.
    • (1996) Ann. Probab , vol.24 , Issue.4 , pp. 1809-1841
    • Gentz, B.1
  • 119
    • 0038956155 scopus 로고    scopus 로고
    • On the central limit theorem for the overlap in the hopfield model
    • Boston, MA: Birkh¨auser Boston
    • B. Gentz. On the central limit theorem for the overlap in the Hopfield model. In Mathematical Aspects of Spin Glasses and Neural Networks, vol. 41 of Progr. Probab, pp. 115–49. Boston, MA: Birkh¨auser Boston, 1998.
    • (1998) Mathematical Aspects of Spin Glasses and Neural Networks , vol.41 , pp. 115-149
    • Gentz, B.1
  • 120
    • 4243067819 scopus 로고    scopus 로고
    • Fluctuations in the hopfield model at the critical temperature
    • B. Gentz and M. Lowe. Fluctuations in the Hopfield model at the critical temperature. Markov Process. Related Fields, 5(4):423–49, 1999.
    • (1999) Markov Process. Related Fields , vol.5 , Issue.4 , pp. 423-449
    • Gentz, B.1    Lowe, M.2
  • 121
    • 0039523934 scopus 로고    scopus 로고
    • The fluctuations of the overlap in the hopfield model with finitely many patterns at the critical temperature
    • B. Gentz and M. Lowe. The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature. Probab. Theory Related Fields, 115(3):357–81, 1999.
    • (1999) Probab. Theory Related Fields , vol.115 , Issue.3 , pp. 357-381
    • Gentz, B.1    Lowe, M.2
  • 122
    • 0001625246 scopus 로고
    • Spontaneous magnetization of randomly dilute ferromagnets
    • H.-O. Georgii. Spontaneous magnetization of randomly dilute ferromagnets. J. Statist. Phys, 25(3):369–96, 1981.
    • (1981) J. Statist. Phys , vol.25 , Issue.3 , pp. 369-396
    • Georgii, H.-O.1
  • 123
    • 0001442164 scopus 로고
    • On the ferromagnetic and the percolative region of random spin systems
    • H.-O. Georgii. On the ferromagnetic and the percolative region of random spin systems. Adv. in Appl. Probab, 16(4):732–65, 1984.
    • (1984) Appl. Probab , vol.16 , Issue.4 , pp. 732-765
    • Georgii, H.-O.1
  • 124
    • 0003723490 scopus 로고
    • Gibbs measures and phase transitions
    • Berlin: Walter de Gruyter & Co
    • H.-O. Georgii. Gibbs Measures and Phase Transitions, vol. 9 of de Gruyter Studies in Mathematics. Berlin: Walter de Gruyter & Co, 1988.
    • (1988) Studies in Mathematics , vol.9
    • Georgii, H.-O.1
  • 125
    • 0034147077 scopus 로고    scopus 로고
    • Percolation and number of phases in the two-dimensional using model
    • H.-O. Georgii and Y. Higuchi. Percolation and number of phases in the two-dimensional Using model. J. Math. Phys, 41(3):1153–69, 2000.
    • (2000) J. Math. Phys , vol.41 , Issue.3 , pp. 1153-1169
    • Georgii, H.-O.1    Higuchi, Y.2
  • 126
    • 0032553281 scopus 로고    scopus 로고
    • General properties of overlap probability distributions in disordered spin systems. Towards parisi ultrametricity
    • S. Ghirlanda and F. Guerra. General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity. J. Phys. A, 31(46):9149–55, 1998.
    • (1998) J. Phys. A , vol.31 , Issue.46 , pp. 9149-9155
    • Ghirlanda, S.1    Guerra, F.2
  • 127
    • 85066663093 scopus 로고
    • Limit theorems for distributions of eigenvalues of random symmetric matrices
    • V. L. Girko. Limit theorems for distributions of eigenvalues of random symmetric matrices. Teor. Veroyatnost. i Mat. Statist, 41:23–9, 129, 1989.
    • (1989) Teor. Veroyatnost. I Mat. Statist , vol.239 , Issue.129 , pp. 41
    • Girko, V.L.1
  • 129
    • 0000125498 scopus 로고
    • Peierls proof of spontaneous magnetization in a two-dimensional using ferromagnet
    • R. B. Griffiths. Peierls proof of spontaneous magnetization in a two-dimensional Using ferromagnet. Phys. Rev. (2), 136:A437–9, 1964.
    • (1964) Phys. Rev , vol.136 , pp. 437-439
    • Griffiths, R.B.1
  • 130
    • 85066670513 scopus 로고    scopus 로고
    • The microcanonical entropy is multiply differentiable. No dinosaurs in microcanonical gravitation
    • D. H. E. Gross. The microcanonical entropy is multiply differentiable. No dinosaurs in microcanonical gravitation. No special microcanonical phase transitions. Preprint condmat/0423582, 2004.
    • (2004) No Special Microcanonical Phase Transitions
    • Gross, D.1
  • 131
    • 0000886046 scopus 로고
    • General properties of polymer systems
    • C. Gruber and H. Kunz. General properties of polymer systems. Comm. Math. Phys, 22:133–61, 1971.
    • (1971) Comm. Math. Phys , vol.22 , pp. 133-161
    • Gruber, C.1    Kunz, H.2
  • 132
    • 0037329695 scopus 로고    scopus 로고
    • Broken replica symmetry bounds in the mean field spin glass model
    • F. Guerra. Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys, 233(1):1–12, 2003.
    • (2003) Comm. Math. Phys , vol.233 , Issue.1 , pp. 1-12
    • Guerra, F.1
  • 133
    • 0036768858 scopus 로고    scopus 로고
    • The thermodynamic limit in mean field spin glass models
    • F. Guerra and F. L. Toninelli. The thermodynamic limit in mean field spin glass models. Comm. Math. Phys, 230(1):71–9, 2002.
    • (2002) Comm. Math. Phys , vol.230 , Issue.1 , pp. 71-79
    • Guerra, F.1    Toninelli, F.L.2
  • 137
    • 0001607313 scopus 로고
    • On the absence of non-translation invariant gibbs states for the two-dimensional using model
    • Amsterdam: North-Holland
    • Y. Higuchi. On the absence of non-translation invariant Gibbs states for the two-dimensional Using model. In Random Fields, Vol. I, II (Esztergom, 1979), vol. 27 of Colloq. Math. Soc. J´anos Bolyai, pp. 517–34. Amsterdam: North-Holland, 1981.
    • (1981) Random Fields , vol.27 , pp. 517-534
    • Higuchi, Y.1
  • 138
    • 0020118274 scopus 로고
    • Neural networks and physical systems with emergent collective computational abilities
    • J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. USA, 79(8):2554–8, 1982.
    • (1982) Proc. Nat. Acad. Sci. USA , vol.79 , Issue.8 , pp. 2554-2558
    • Hopfield, J.J.1
  • 139
    • 32844459049 scopus 로고
    • Calculation of partition functions
    • J. Hubbard. Calculation of partition functions. Phys. Rev. Lett, 3:77–8, 1959.
    • (1959) Phys. Rev. Lett , vol.3 , pp. 77-78
    • Hubbard, J.1
  • 140
    • 25544445134 scopus 로고
    • Pure states in spin glasses
    • D. A. Huse and D. S. Fisher. Pure states in spin glasses. J. Phys. A, 20(15):L997–1003, 1987.
    • (1987) J. Phys. A , vol.20 , Issue.15 , pp. 997-1003
    • Huse, D.A.1    Fisher, D.S.2
  • 141
    • 0000941582 scopus 로고
    • Random-field instability of the ordered state of continuous symmetry
    • Y. Imry and S. Ma. Random-field instability of the ordered state of continuous symmetry. Phys. Rev. Lett, 35:1399–401, 1975.
    • (1975) Phys. Rev. Lett , vol.35 , pp. 1399-1401
    • Imry, Y.1    Ma, S.2
  • 142
    • 0032270185 scopus 로고    scopus 로고
    • Dobrushin–koteck´y–shlosman theorem up to the critical temperature
    • D. Ioffe and R. H. Schonmann. Dobrushin–Koteck´y–Shlosman theorem up to the critical temperature. Comm. Math. Phys, 199(1):117–67, 1998.
    • (1998) Comm. Math. Phys , vol.199 , Issue.1 , pp. 117-167
    • Ioffe, D.1    Schonmann, R.H.2
  • 148
    • 1542354916 scopus 로고
    • The statistical mechanical theory of melecular distribution functions in liquids
    • J. G. Kirkwood and Z.W. Salsburg. The statistical mechanical theory of melecular distribution functions in liquids. Discussions Farday Soc, 15:28–34, 1953.
    • (1953) Discussions Farday Soc , vol.15 , pp. 28-34
    • Kirkwood, J.G.1    Salsburg, Z.W.2
  • 149
    • 0031521188 scopus 로고    scopus 로고
    • Taming griffiths’ singularities in long range randomising models
    • A. Klein and S. Masooman. Taming Griffiths’ singularities in long range randomising models. Comm. Math. Phys, 189(2):497–512, 1997.
    • (1997) Comm. Math. Phys , vol.189 , Issue.2 , pp. 497-512
    • Klein, A.1    Masooman, S.2
  • 150
    • 85066681797 scopus 로고    scopus 로고
    • Ernst ising, physicist and teacher
    • S. Kobe. Ernst Ising, physicist and teacher. J. Phys. Stud, 2(1):1–2, 1998.
    • (1998) J. Phys. Stud , vol.2 , Issue.1 , pp. 1-2
    • Kobe, S.1
  • 151
    • 21144471119 scopus 로고
    • A free energy bound for the hopfield model
    • H. Koch. A free energy bound for the Hopfield model. J. Phys. A, 26(6):L353–5, 1993.
    • (1993) J. Phys. A , vol.26 , Issue.6 , pp. 353-355
    • Koch, H.1
  • 152
    • 0039523078 scopus 로고
    • Some rigorous results on the hopfield neural network model
    • H. Koch and J. Piasko. Some rigorous results on the Hopfield neural network model. J. Statist. Phys, 55(5–6):903–28, 1989.
    • (1989) J. Statist. Phys , vol.55 , Issue.5-6 , pp. 903-928
    • Koch, H.1    Piasko, J.2
  • 153
    • 0023829082 scopus 로고
    • Convergence results in a autoassociative memory model
    • J. Komlos and R. Paturi. Convergence results in a autoassociative memory model. Neural Networks, 1:239–50, 1988.
    • (1988) Neural Networks , vol.1 , pp. 239-250
    • Komlos, J.1    Paturi, R.2
  • 154
    • 0000639657 scopus 로고
    • Cluster expansion for abstract polymer models
    • R. Kotecky and D. Preiss. Cluster expansion for abstract polymer models. Comm. Math. Phys, 103(3):491–8, 1986.
    • (1986) Comm. Math. Phys , vol.103 , Issue.3 , pp. 491-498
    • Kotecky, R.1    Preiss, D.2
  • 155
    • 26844560535 scopus 로고    scopus 로고
    • A representation of gibbs measure for the random energy model
    • M. F. Kratz and P. Picco. A representation of Gibbs measure for the random energy model. Ann. Appl. Probab, 14(2):651–77, 2004.
    • (2004) Ann. Appl. Probab , vol.14 , Issue.2 , pp. 651-677
    • Kratz, M.F.1    Picco, P.2
  • 156
    • 0040453759 scopus 로고    scopus 로고
    • Metastates in disordered mean-field models: Random field and hopfield models
    • C. Kulske. Metastates in disordered mean-field models: random field and Hopfield models. J. Statist. Phys, 88(5–6):1257–93, 1997.
    • (1997) J. Statist. Phys , vol.88 , Issue.5-6 , pp. 1257-1293
    • Kulske, C.1
  • 157
    • 0032045210 scopus 로고    scopus 로고
    • Metastates in disordered mean-field models
    • C. Kulske. Metastates in disordered mean-field models. II. The super states. J. Statist. Phys, 91(1–2):155–76, 1998.
    • (1998) The Super States. J. Statist. Phys , vol.91 , Issue.1-2 , pp. 155-176
    • Kulske, C.1
  • 158
    • 0035624973 scopus 로고    scopus 로고
    • Weakly gibbsian representations for joint measures of quenched lattice spin models
    • C. Kulske. Weakly Gibbsian representations for joint measures of quenched lattice spin models. Probab. Theory Related Fields, 119(1):1–30, 2001.
    • (2001) Probab. Theory Related Fields , vol.119 , Issue.1 , pp. 1-30
    • Kulske, C.1
  • 159
    • 0347753617 scopus 로고    scopus 로고
    • Analogues of non-gibbsianness in joint measures of disordered mean-field models
    • C. Kulske. Analogues of non-Gibbsianness in joint measures of disordered mean-field models. J. Statist. Phys, 112(5–6):1079–108, 2003.
    • (2003) J. Statist. Phys , vol.112 , Issue.5-6 , pp. 1079-1108
    • Kulske, C.1
  • 160
    • 0000799233 scopus 로고
    • Observables at infinity and states with short range correlations in statistical mechanics
    • O. E. Lanford, and D. Ruelle. Observables at infinity and states with short range correlations in statistical mechanics. Comm. Math. Phys, 13:194–215, 1969.
    • (1969) Comm. Math. Phys , vol.13 , pp. 194-215
    • Lanford, O.E.1    Ruelle, D.2
  • 161
    • 0003910552 scopus 로고
    • Extremes and related properties of random sequences and processes
    • New York: Springer-Verlag
    • M. R. Leadbetter, G. Lindgren, and H. Rootzen. Extremes and Related Properties of Random Sequences and Processes. Springer Series in Statistics. New York: Springer-Verlag, 1983.
    • (1983) Springer Series in Statistics
    • Leadbetter, M.R.1    Lindgren, G.2    Rootzen, H.3
  • 162
    • 0001742454 scopus 로고
    • On the uniqueness of the equilibrium state for using spin systems
    • J. L. Lebowitz and A. Martin-Lnof. On the uniqueness of the equilibrium state for Using spin systems. Comm. Math. Phys, 25:276–82, 1972.
    • (1972) Comm. Math. Phys , vol.25 , pp. 276-282
    • Lebowitz, J.L.1    Martin-Lnof, A.2
  • 163
    • 0033095116 scopus 로고    scopus 로고
    • Liquid. Vapor phase transitions for systems with finite-range interactions
    • J. L. Lebowitz, A. Mazel, and E. Presutti. Liquid.vapor phase transitions for systems with finite-range interactions. J. Statist. Phys, 94(5–6):955–1025, 1999.
    • (1999) J. Statist. Phys , vol.94 , Issue.5-6 , pp. 955-1025
    • Lebowitz, J.L.1    Mazel, A.2    Presutti, E.3
  • 164
    • 11544338334 scopus 로고    scopus 로고
    • Improved peierls argument for high-dimensional using models
    • J. L. Lebowitz and A. E. Mazel. Improved Peierls argument for high-dimensional Using models. J. Statist. Phys, 90(3–4):1051–9, 1998.
    • (1998) J. Statist. Phys , vol.90 , Issue.3-4 , pp. 1051-1059
    • Lebowitz, J.L.1    Mazel, A.E.2
  • 165
    • 0034343879 scopus 로고    scopus 로고
    • On the distribution of overlaps in the sherrington. Kirkpatrick spin glass model
    • M. Ledoux. On the distribution of overlaps in the Sherrington.Kirkpatrick spin glass model. J. Statist. Phys, 100(5–6):871–92, 2000.
    • (2000) J. Statist. Phys , vol.100 , Issue.5-6 , pp. 871-892
    • Ledoux, M.1
  • 166
    • 0003771756 scopus 로고
    • Probability in banach spaces
    • Berlin: Springer-Verlag
    • M. Ledoux and M. Talagrand. Probability in Banach Spaces, vol. 23 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Berlin: Springer-Verlag, 1991.
    • (1991) Results in Mathematics and Related Areas , vol.23
    • Ledoux, M.1    Talagrand, M.2
  • 167
    • 24544478297 scopus 로고
    • Exact solution of the problem of the entropy of two-dimensional ice
    • E. H. Lieb. Exact solution of the problem of the entropy of two-dimensional ice. Phys. Rev. Lett, 18(17):692–4, 1967.
    • (1967) Phys. Rev. Lett , vol.18 , Issue.17 , pp. 692-694
    • Lieb, E.H.1
  • 168
    • 0001930137 scopus 로고    scopus 로고
    • The physics and mathematics of the second law of thermodynamics
    • E. H. Lieb and J. Yngvason. The physics and mathematics of the second law of thermodynamics. Phys. Rep, 310(1):96, 1999.
    • (1999) Phys. Rep , vol.310 , Issue.1 , pp. 96
    • Lieb, E.H.1    Yngvason, J.2
  • 169
    • 0031074948 scopus 로고    scopus 로고
    • Lower bounds on the restitution error in the hopfield model
    • D. Loukianova. Lower bounds on the restitution error in the Hopfield model. Probab. Theory Related Fields, 107(2):161–76, 1997.
    • (1997) Probab. Theory Related Fields , vol.107 , Issue.2 , pp. 161-176
    • Loukianova, D.1
  • 170
    • 0002358783 scopus 로고    scopus 로고
    • Almost gibbsian versus weakly gibbsian measures
    • C. Maes, F. Redig, and A. Van Moffaert. Almost Gibbsian versus weakly Gibbsian measures. Stochastic Process. Appl, 79(1):1–15, 1999.
    • (1999) Stochastic Process. Appl , vol.79 , Issue.1 , pp. 1-15
    • Maes, C.1    Redig, F.2    Van Moffaert, A.3
  • 171
    • 85066646462 scopus 로고
    • Complete cluster expansions for weakly coupled gibbs random fields
    • New York: Dekker
    • V. A. Malyshev. Complete cluster expansions for weakly coupled Gibbs random fields. In Multicomponent Random Systems, vol. 6 of Adv. Probab. Related Topics, pp. 505–530. New York: Dekker, 1980.
    • (1980) Multicomponent Random Systems , vol.6 , pp. 505-530
    • Malyshev, V.A.1
  • 172
    • 0000263234 scopus 로고
    • Distribution of eigenvalues in certain sets of random matrices
    • V. A. Marcenko and L. A. Pastur. Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N. S.), 72(114):507–36, 1967.
    • (1967) Mat. Sb , vol.72 , Issue.114 , pp. 507-536
    • Marcenko, V.A.1    Pastur, L.A.2
  • 173
    • 12344318004 scopus 로고
    • Solvable spin system with random interactions
    • D. C. Mattis. Solvable spin system with random interactions. Phys. Lett, 56(1):421–2, 1976.
    • (1976) Phys. Lett , vol.56 , Issue.1 , pp. 421-422
    • Mattis, D.C.1
  • 174
    • 0003786097 scopus 로고
    • Berlin, Heidelberg: Springer-Verlag
    • J. E. Mayer. Handbuch der Physik. Berlin, Heidelberg: Springer-Verlag, 1958.
    • (1958) Handbuch Der Physik
    • Mayer, J.E.1
  • 175
    • 51249194645 scopus 로고
    • A logical calculus of the ideas immanent in nervous activity
    • W. S McCulloch and W. Pitts. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophysics, 5:115–33, 1943.
    • (1943) Bull. Math. Biophysics , vol.5 , pp. 115-133
    • McCulloch, W.S.1    Pitts, W.2
  • 176
    • 0000476374 scopus 로고    scopus 로고
    • Phase transition in the number partitioning problem
    • St. Mertens. Phase transition in the number partitioning problem. Phys. Rev. Lett, 81(20):4281-4, 1998.
    • (1998) Phys. Rev. Lett , vol.81 , Issue.20 , pp. 4281-4284
    • Mertens, S.T.1
  • 177
    • 0034887263 scopus 로고    scopus 로고
    • A physicist's approach to number partitioning
    • St. Mertens. A physicist's approach to number partitioning. Theoret. Comput. Sci, 265(1–2):79–108, 2001.
    • (2001) Theoret. Comput. Sci , vol.265 , Issue.1-2 , pp. 79-108
    • Mertens, S.T.1
  • 179
    • 0033745417 scopus 로고    scopus 로고
    • On the convergence of cluster expansions
    • S. Miracle-Sole. On the convergence of cluster expansions. Phys. A, 279(1–4):244–9, 2000.
    • (2000) Phys. A , vol.279 , Issue.1-4 , pp. 244-249
    • Miracle-Sole, S.1
  • 180
    • 0033211776 scopus 로고    scopus 로고
    • On the using model with strongly anisotropic external field
    • F. R. Nardi, E. Olivieri, and M. Zahradnýk. On the Using model with strongly anisotropic external field. J. Statist. Phys, 97(1–2):87–144, 1999.
    • (1999) J. Statist. Phys , vol.97 , Issue.1-2 , pp. 87-144
    • Nardi, F.R.1    Olivieri, E.2    Zahradnýk, M.3
  • 181
    • 0038056172 scopus 로고
    • A continuous state branching process in relation with the grem model of spin glass theory
    • Ecole Polytechnique Paris
    • J. Neveu. A continuous state branching process in relation with the GREM model of spin glass theory. Rapport interne 267, Ecole Polytechnique Paris, 1992.
    • (1992) Rapport Interne , vol.267
    • Neveu, J.1
  • 182
    • 4244055093 scopus 로고    scopus 로고
    • Simplicity of state and overlap structure in finite-volume realistic spin glasses
    • C. M. Newman and D. L. Stein. Simplicity of state and overlap structure in finite-volume realistic spin glasses. Phys. Rev. E (3), 57(2, part A):1356–66, 1998.
    • (1998) Phys. Rev. E , vol.57 , Issue.3 , pp. 1356-1366
    • Newman, C.M.1    Stein, D.L.2
  • 183
    • 0023869164 scopus 로고
    • Memory capacity in neural network
    • C. M. Newman. Memory capacity in neural network. Neural Networks, 1:223–38, 1988.
    • (1988) Neural Networks , vol.1 , pp. 223-238
    • Newman, C.M.1
  • 185
    • 0040358565 scopus 로고
    • Chaotic size dependence in spin glasses
    • Dordrecht: Kluwer Academic Publishers
    • C. M. Newman and D. L. Stein. Chaotic size dependence in spin glasses. In Cellular Automata and Cooperative Systems (Les Houches, 1992), vol. 396 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, pp. 525–9. Dordrecht: Kluwer Academic Publishers, 1993.
    • (1993) Cellular Automata and Cooperative Systems , vol.396 , pp. 525-529
    • Newman, C.M.1    Stein, D.L.2
  • 186
    • 0007010715 scopus 로고    scopus 로고
    • Thermodynamic chaos and the structure of short-range spin glasses
    • Boston, MA: Birkh¨auser Boston
    • C. M. Newman and D. L. Stein. Thermodynamic chaos and the structure of short-range spin glasses. In Mathematical Aspects of Spin Glasses and Neural Networks, vol. 41 of Progr. Probab, pp. 243–287. Boston, MA: Birkh¨auser Boston, 1998.
    • (1998) Mathematical Aspects of Spin Glasses and Neural Networks , vol.41 , pp. 243-287
    • Newman, C.M.1    Stein, D.L.2
  • 187
    • 0033070887 scopus 로고    scopus 로고
    • Equilibrium pure states and non equilibrium chaos
    • C. M. Newman and D. L. Stein. Equilibrium pure states and non equilibrium chaos. J. Statist. Phys, 94(3–4):709–22, 1999.
    • (1999) J. Statist. Phys , vol.94 , Issue.3-4 , pp. 709-722
    • Newman, C.M.1    Stein, D.L.2
  • 188
    • 0013248235 scopus 로고    scopus 로고
    • Metastable states in spin glasses and disordered ferromagnets
    • C. M. Newman and D. L. Stein. Metastable states in spin glasses and disordered ferromagnets. Phys. Rev. E (3), 60(5, part A):5244–60, 1999.
    • (1999) Phys. Rev. E , vol.60 , Issue.3 , pp. 5244-5260
    • Newman, C.M.1    Stein, D.L.2
  • 189
    • 85066654877 scopus 로고    scopus 로고
    • Short-range spin glasses: A status report
    • Cambridge, MA: International Press
    • C. M. Newman and D. L. Stein. Short-range spin glasses: a status report. In XIIth International Congress of Mathematical Physics (ICMP’97) (Brisbane), pp. 167–172. Cambridge, MA: International Press, 1999.
    • (1999) Xiith International Congress of Mathematical Physics , pp. 167-172
    • Newman, C.M.1    Stein, D.L.2
  • 192
    • 0003689287 scopus 로고    scopus 로고
    • Statistical physics of spin glasses and information processing
    • Oxford: Oxford University Press
    • H. Nishimori. Statistical Physics of Spin Glasses and Information Processing. International Series of Monographs on Physics 111. Oxford: Oxford University Press, 2001.
    • (2001) International Series of Monographs on Physics , vol.111
    • Nishimori, H.1
  • 193
    • 0001132742 scopus 로고
    • On the existence of thermodynamics for the random energy model
    • E. Olivieri and P. Picco. On the existence of thermodynamics for the random energy model. Comm. Math. Phys, 96(1):125–44, 1984.
    • (1984) Comm. Math. Phys , vol.96 , Issue.1 , pp. 125-144
    • Olivieri, E.1    Picco, P.2
  • 194
    • 36149012281 scopus 로고
    • Crystal statistics, i. A two-dimensional model with an order-disorder transition
    • L. Onsager. Crystal statistics, I. A two-dimensional model with an order-disorder transition. Phys. Rev, 65:117–49, 1944.
    • (1944) Phys. Rev , vol.65 , pp. 117-149
    • Onsager, L.1
  • 195
    • 33744743865 scopus 로고
    • Random magnetic fields, supersymmetry, and negative dimensions
    • G. Parisi and N. Sourlas. Random magnetic fields, supersymmetry, and negative dimensions. Phys. Rev. Lett, 43(11):744–5, 1979.
    • (1979) Phys. Rev. Lett , vol.43 , Issue.11 , pp. 744-745
    • Parisi, G.1    Sourlas, N.2
  • 196
    • 0010011477 scopus 로고
    • Exactly soluble model of a spin glass
    • L. A. Pastur and A. L. Figotin. Exactly soluble model of a spin glass. Sov. J. Low Temp. Phys, 3(6):378–83, 1977.
    • (1977) Sov. J. Low Temp. Phys , vol.3 , Issue.6 , pp. 378-383
    • Pastur, L.A.1    Figotin, A.L.2
  • 197
    • 54749144929 scopus 로고
    • On the theory of disordered spin systems
    • L. A. Pastur and A. L. Figotin. On the theory of disordered spin systems. Teoret. Mat. Fiz, 35(2):193–210, 1978.
    • (1978) Teoret. Mat. Fiz , vol.35 , Issue.2 , pp. 193-210
    • Pastur, L.A.1    Figotin, A.L.2
  • 198
    • 84868027552 scopus 로고
    • Limit of the infinite range of interaction for a class of disordered systems
    • L. A. Pastur and A. L. Figotin. Limit of the infinite range of interaction for a class of disordered systems. Teoret. Mat. Fiz, 51(3):380–8, 1982.
    • (1982) Teoret. Mat. Fiz , vol.51 , Issue.3 , pp. 380-388
    • Pastur, L.A.1    Figotin, A.L.2
  • 199
    • 21344485673 scopus 로고
    • The replica-symmetric solution without replica trick for the hopfield model
    • L. A. Pastur, M. Shcherbina, and B. Tirozzi. The replica-symmetric solution without replica trick for the Hopfield model. J. Statist. Phys, 74(5–6):1161–83, 1994.
    • (1994) J. Statist. Phys , vol.74 , Issue.5-6 , pp. 1161-1183
    • Pastur, L.A.1    Shcherbina, M.2    Tirozzi, B.3
  • 200
    • 84924799755 scopus 로고
    • On ising's model of ferromagnetism
    • R. Peierls. On Ising's model of ferromagnetism. Proc. Cambridge Philos. Soc, 32:477–81, 1936.
    • (1936) Proc. Cambridge Philos. Soc , vol.32 , pp. 477-481
    • Peierls, R.1
  • 201
    • 3543145997 scopus 로고    scopus 로고
    • Thermodynamic formalism of neural computing
    • Dordrecht: Kluwer Academic Publishers
    • D. Petritis. Thermodynamic formalism of neural computing. In Dynamics of Complex Interacting Systems (Santiago, 1994), vol. 2 of Nonlinear Phenom. Complex Systems, pp. 81–146. Dordrecht: Kluwer Academic Publishers, 1996.
    • (1996) Dynamics of Complex Interacting Systems , vol.2 , pp. 81-146
    • Petritis, D.1
  • 202
    • 0141507622 scopus 로고    scopus 로고
    • Thermodynamical aspects of classical lattice systems
    • Boston, MA: Birkh¨auser Boston
    • C.-E. Pfister. Thermodynamical aspects of classical lattice systems. In In and Out of Equilibrium (Mambucaba, 2000), vol. 51 of Progr. Probab, pp. 393–472. Boston, MA: Birkh¨auser Boston, 2002.
    • (2002) And out of Equilibrium , vol.51 , pp. 393-472
    • Pfister, C.-E.1
  • 203
    • 0002749724 scopus 로고
    • Phase diagrams of classical lattice systems
    • S. A. Pirogov and Ja. G. Sinai. Phase diagrams of classical lattice systems. Teoret. Mat. Fiz, 25(3):358–69, 1975.
    • (1975) Teoret. Mat. Fiz , vol.25 , Issue.3 , pp. 358-369
    • Pirogov, S.A.1    Sinai, J.G.2
  • 204
    • 0002749722 scopus 로고
    • Phase diagrams of classical lattice systems
    • S. A. Pirogov and Ja. G. Sinai. Phase diagrams of classical lattice systems. (Continuation). Teoret. Mat. Fiz, 26(1):61–76, 1976.
    • (1976) Teoret. Mat. Fiz , vol.26 , Issue.1 , pp. 61-76
    • Pirogov, S.A.1    Sinai, J.G.2
  • 206
    • 0003612621 scopus 로고
    • Gibbs states on countable sets
    • London: Cambridge University Press
    • C. J. Preston. Gibbs States on Countable Sets. Cambridge Tracts in Mathematics, No. 68. London: Cambridge University Press, 1974.
    • (1974) Cambridge Tracts in Mathematics , Issue.68
    • Preston, C.J.1
  • 208
    • 85066682743 scopus 로고    scopus 로고
    • Scaling limits in statistical mechanics and microstructures in continuum mechanics
    • E. Presutti. Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics. In Preparation, 2005.
    • (2005) Preparation
    • Presutti, E.1
  • 212
    • 0000246287 scopus 로고
    • Classical statistical mechanics of a system of particles
    • D. Ruelle. Classical statistical mechanics of a system of particles. Helv. Phys. Acta, 36:183–97, 1963.
    • (1963) Helv. Phys. Acta , vol.36 , pp. 183-197
    • Ruelle, D.1
  • 214
  • 215
    • 0000545781 scopus 로고
    • A mathematical reformulation of derrida's rem and grem
    • D. Ruelle. A mathematical reformulation of Derrida's REM and GREM. Comm. Math. Phys, 108(2):225–39, 1987.
    • (1987) Comm. Math. Phys , vol.108 , Issue.2 , pp. 225-239
    • Ruelle, D.1
  • 216
    • 0141673308 scopus 로고    scopus 로고
    • Some ill-formulated problems on regular and messy behavior in statistical mechanics and smooth dynamics for which i would like the advice of yasha sinai
    • D. Ruelle. Some ill-formulated problems on regular and messy behavior in statistical mechanics and smooth dynamics for which I would like the advice of Yasha Sinai. J. Statist. Phys, 108(5–6):723–8, 2002.
    • (2002) J. Statist. Phys , vol.108 , Issue.5-6 , pp. 723-728
    • Ruelle, D.1
  • 217
    • 14944383950 scopus 로고    scopus 로고
    • Characterization of invariant measures at the leading edge for competing particle systems
    • A. Ruzmaikina and M. Aizenman. Characterization of invariant measures at the leading edge for competing particle systems. Ann. Probab, 33(1):82–113, 2005.
    • (2005) Ann. Probab , vol.33 , Issue.1 , pp. 82-113
    • Ruzmaikina, A.1    Aizenman, M.2
  • 218
    • 17544380550 scopus 로고    scopus 로고
    • The repulsive lattice gas, the independent set polynomials, and the lovasz local lemma
    • A. Scott and A. D. Sokal. The repulsive lattice gas, the independent set polynomials, and the Lovasz local lemma. J. Statist. Phys, 118:1151–261, 2005.
    • (2005) J. Statist. Phys , vol.118 , pp. 1151-1261
    • Scott, A.1    Sokal, A.D.2
  • 219
    • 21144472818 scopus 로고
    • The free energy of a class of hopfield models
    • M. Shcherbina and B. Tirozzi. The free energy of a class of Hopfield models. J. Statist. Phys, 72(1–2):113–25, 1993.
    • (1993) J. Statist. Phys , vol.72 , Issue.1-2 , pp. 113-125
    • Shcherbina, M.1    Tirozzi, B.2
  • 220
    • 4444384303 scopus 로고
    • Solvable model of a spin glass
    • D. Sherrington and S. Kirkpatrick. Solvable model of a spin glass. Phys. Rev. Letts, 35: 1792–96, 1972.
    • (1972) Rev. Letts , vol.35 , pp. 1792-1796
    • Sherrington, D.1    Kirkpatrick, S.2
  • 222
    • 0001427422 scopus 로고
    • Eigenvalues and eigenvectors of large-dimensional sample covariance matrices
    • Providence, RI: American Mathematical Society
    • J.W. Silverstein. Eigenvalues and eigenvectors of large-dimensional sample covariance matrices. In Random Matrices and their Applications (Brunswick, ME, 1984), vol. 50 of Contemp. Math, pp. 153–9. Providence, RI: American Mathematical Society, 1986.
    • (1986) Random Matrices and Their Applications , vol.50 , pp. 153-159
    • Silverstein, J.W.1
  • 223
    • 0003426810 scopus 로고
    • The statistical mechanics of lattice gases
    • Princeton, NJ: Princeton University Press
    • B. Simon. The statistical mechanics of lattice gases. Vol. 1. Princeton Series in Physics. Princeton, NJ: Princeton University Press, 1993.
    • (1993) Princeton Series in Physics , vol.1
    • Simon, B.1
  • 224
    • 0001200214 scopus 로고
    • On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics
    • J. G. Sinai. On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics. Soviet Math. Dokl, 4:1818–22, 1963.
    • (1963) Soviet Math. Dokl , vol.4 , pp. 1818-1822
    • Sinai, J.G.1
  • 225
    • 0003552704 scopus 로고
    • Theory of phase transitions: Rigorous results
    • Oxford: Pergamon Press
    • Y. G. Sinai. Theory of Phase transitions: Rigorous Results, vol. 108 of International Series in Natural Philosophy. Oxford: Pergamon Press, 1982.
    • (1982) International Series in Natural Philosophy , vol.108
    • Sinai, Y.G.1
  • 226
    • 84944485006 scopus 로고
    • The one-sided barrier problem for gaussian noise
    • D. Slepian. The one-sided barrier problem for Gaussian noise. Bell System Tech. J, 41:463–501, 1962.
    • (1962) Bell System Tech. J , vol.41 , pp. 463-501
    • Slepian, D.1
  • 227
    • 0033727834 scopus 로고    scopus 로고
    • Chromatic polynomials, potts models, and all that
    • A. D. Sokal. Chromatic polynomials, potts models, and all that. Physica A, 279:324–32, 1999.
    • (1999) Physica A , vol.279 , pp. 324-332
    • Sokal, A.D.1
  • 229
    • 0001548540 scopus 로고
    • A method for the computation of quantum distribution functions
    • R. L. Stratonovic. A method for the computation of quantum distribution functions. Dokl. Akad. Nauk SSSR (N.S.), 115:1097–100, 1957.
    • (1957) Dokl. Akad. Nauk SSSR , vol.115 , pp. 1097-1100
    • Stratonovic, R.L.1
  • 230
    • 51249165477 scopus 로고
    • Concentration of measure and isoperimetric inequalities in product spaces
    • M. Talagrand. Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes E´tudes Sci. Publ. Math, 81:73–205, 1995.
    • (1995) Inst. Hautes E´tudes Sci. Publ. Math , vol.81 , pp. 73-205
    • Talagrand, M.1
  • 231
    • 0030522124 scopus 로고    scopus 로고
    • A new look at independence
    • M. Talagrand. A new look at independence. Ann. Probab, 24(1):1–34, 1996.
    • (1996) Ann. Probab , vol.24 , Issue.1 , pp. 1-34
    • Talagrand, M.1
  • 232
    • 0009148982 scopus 로고    scopus 로고
    • Rigorous results for the hopfield model with many patterns
    • M. Talagrand. Rigorous results for the Hopfield model with many patterns. Probab. Theory Related Fields, 110(2):177–276, 1998.
    • (1998) Probab. Theory Related Fields , vol.110 , Issue.2 , pp. 177-276
    • Talagrand, M.1
  • 233
    • 0031995245 scopus 로고    scopus 로고
    • The sherrington–kirkpatrick model: A challenge for mathematicians
    • M. Talagrand. The Sherrington–Kirkpatrick model: a challenge for mathematicians. Probab. Theory Related Fields, 110(2):109–76, 1998.
    • (1998) Probab. Theory Related Fields , vol.110 , Issue.2 , pp. 109-176
    • Talagrand, M.1
  • 234
    • 0034558587 scopus 로고    scopus 로고
    • Exponential inequalities and convergence of moments in the replica-symmetric regime of the hopfield model
    • M. Talagrand. Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model. Ann. Probab, 28(4):1393–469, 2000.
    • (2000) Ann. Probab , vol.28 , Issue.4 , pp. 1393-1469
    • Talagrand, M.1
  • 235
    • 0034391871 scopus 로고    scopus 로고
    • Rigorous low-temperature results for the mean field p-spins interaction model
    • M. Talagrand. Rigorous low-temperature results for the mean field p-spins interaction model. Probab. Theory Related Fields, 117(3):303–60, 2000.
    • (2000) Probab. Theory Related Fields , vol.117 , Issue.3 , pp. 303-360
    • Talagrand, M.1
  • 236
    • 0036437265 scopus 로고    scopus 로고
    • Gaussian averages, bernoulli averages, and gibbs’ measures
    • M. Talagrand. Gaussian averages, Bernoulli averages, and Gibbs’ measures. Random Structures Algorithms, 21(3–4):197–204, 2002.
    • (2002) Random Structures Algorithms , vol.21 , Issue.3-4 , pp. 197-204
    • Talagrand, M.1
  • 237
    • 0037340681 scopus 로고    scopus 로고
    • Self organization in the low temperature phase of a spin glass model
    • M. Talagrand. Self organization in the low temperature phase of a spin glass model. Rev. Math. Phys, 14:1–78, 2003.
    • (2003) Rev. Math. Phys , vol.14 , pp. 1-78
    • Talagrand, M.1
  • 238
    • 0004313816 scopus 로고    scopus 로고
    • Spin glasses: A challenge for mathematicians
    • Berlin: Springer-Verlag
    • M. Talagrand. Spin Glasses: a Challenge for Mathematicians, vol. 46 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Berlin: Springer-Verlag, 2003.
    • (2003) Results in Mathematics and Related Areas , vol.46
    • Talagrand, M.1
  • 239
    • 85066640054 scopus 로고    scopus 로고
    • The parisi solution
    • M. Talagrand. The Parisi solution. Ann. Math, to appear, 2005.
    • (2005) Ann. Math
    • Talagrand, M.1
  • 241
    • 29144463870 scopus 로고    scopus 로고
    • Cluster expansions and correlation functions
    • D. Ueltschi. Cluster expansions and correlation functions. Mosc. Math. J, 4(2):511–522, 576, 2004.
    • (2004) Mosc. Math. J , vol.4 , Issue.2 , pp. 511-522
    • Ueltschi, D.1
  • 242
    • 0001789901 scopus 로고
    • Interface sharpness in using systems
    • H. van Beijeren. Interface sharpness in using systems. Comm. Math. Phys, 40:1–6, 1975.
    • (1975) Comm. Math. Phys , vol.40 , pp. 1-6
    • Van Beijeren, H.1
  • 243
    • 0000061166 scopus 로고
    • Disagreement percolation in the study of markov fields
    • J. van den Berg and C. Maes. Disagreement percolation in the study of Markov fields. Ann. Probab, 22(2):749–63, 1994.
    • (1994) Ann. Probab , vol.22 , Issue.2 , pp. 749-763
    • Van Den Berg, J.1    Maes, C.2
  • 244
    • 0346705146 scopus 로고    scopus 로고
    • The griffiths singularity random field
    • Providence, RI: American Mathematical Society
    • A. van Enter, C. Maes, R. H. Schonmann, and S. Shlosman. The Griffiths singularity random field. In On Dobrushin'sWay. From Probability Theory to Statistical Physics, vol. 198 of Amer. Math. Soc. Transl. Ser. 2, pp. 51–58. Providence, RI: American Mathematical Society, 2000.
    • (2000) From Probability Theory to Statistical Physics , vol.198 , pp. 51-58
    • Van Enter, A.1    Maes, C.2    Schonmann, R.H.3    Shlosman, S.4
  • 245
    • 17444397825 scopus 로고    scopus 로고
    • Chaotic size dependence in the using model with random boundary conditions
    • A. C. D. van Enter, I. Medved’, and K. Netocny. Chaotic size dependence in the Using model with random boundary conditions. Markov Process. Related Fields, 8(3):479–508, 2002.
    • (2002) Markov Process. Related Fields , vol.8 , Issue.3 , pp. 479-508
    • Van Enter, A.1    Medved’, I.2    Netocny, K.3
  • 246
    • 17444382680 scopus 로고    scopus 로고
    • On the using model with random boundary conditions
    • A. C. D. van Enter, K. Netocny, and H. G. Schaap. On the using model with random boundary conditions. Jour. Stat. Phys, 118:997–1056, 2005.
    • (2005) Jour. Stat. Phys , vol.118 , pp. 997-1056
    • Van Enter, A.1    Netocny, K.2    Schaap, H.G.3
  • 247
    • 0037155766 scopus 로고    scopus 로고
    • Infinitely many states and stochastic symmetry in a gaussian potts–hopfield model
    • A. C. D. van Enter and H. G. Schaap. Infinitely many states and stochastic symmetry in a Gaussian Potts–Hopfield model. J. Phys. A, 35(11):2581–92, 2002.
    • (2002) J. Phys. A , vol.35 , Issue.11 , pp. 2581-2592
    • Van Enter, A.1    Schaap, H.G.2
  • 248
    • 0002924101 scopus 로고
    • The thermodynamic limit for long-range random systems
    • A. C. D. van Enter and J. L. van Hemmen. The thermodynamic limit for long-range random systems. J. Statist. Phys, 32(1):141–52, 1983.
    • (1983) J. Statist. Phys , vol.32 , Issue.1 , pp. 141-152
    • Van Enter, A.1    Van Hemmen, J.L.2
  • 249
    • 34250084304 scopus 로고
    • Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of gibbsian theory
    • A. C. D. van Enter, R. Fernandez, and A. D. Sokal. Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory. J. Statist. Phys, 72(5–6):879–1167, 1993.
    • (1993) J. Statist. Phys , vol.72 , Issue.5-6 , pp. 879-1167
    • Van Enter, A.1    Fernandez, R.2    Sokal, A.D.3
  • 250
    • 0042763474 scopus 로고
    • The order parameter in a spin glass
    • A. C. D. van Enter and R. B. Griffiths. The order parameter in a spin glass. Comm. Math. Phys, 90(3):319–27, 1983.
    • (1983) Comm. Math. Phys , vol.90 , Issue.3 , pp. 319-327
    • Van Enter, A.1    Griffiths, R.B.2
  • 251
    • 24244450351 scopus 로고
    • Chopper model for pattern recognition
    • A. C. D. van Enter and J. L. van Hemmen. Chopper model for pattern recognition. Phys. Rev, 34(A):2509–12, 1986.
    • (1986) Phys. Rev , vol.34 , pp. 2509-2512
    • Van Enter, A.1    Van Hemmen, J.L.2
  • 252
    • 77249131934 scopus 로고
    • Equilibrium theory of spin glasses: Mean-field theory and beyond
    • Berlin: Springer-Verlag
    • J. L. van Hemmen. Equilibrium theory of spin glasses: mean-field theory and beyond. In Heidelberg Colloquium on Spin Glasses (Heidelberg, 1983), vol. 192 of Lecture Notes in Phys, pp. 203–33. Berlin: Springer-Verlag, 1983.
    • (1983) Heidelberg Colloquium on Spin Glasses , vol.192 , pp. 203-233
    • Van Hemmen, J.L.1
  • 253
    • 4243283914 scopus 로고
    • Spin-glass models of a neural network
    • J. L. van Hemmen. Spin-glass models of a neural network. Phys. Rev. A (3), 34(4):3435–45, 1986.
    • (1986) Phys. Rev. A , vol.34 , Issue.4 , pp. 3435-3445
    • Van Hemmen, J.L.1
  • 254
    • 0002091221 scopus 로고
    • Elementary solution of classical spin-glass models
    • J. L. van Hemmen, D. Grensing, A. Huber, and R. Kuhn. Elementary solution of classical spin-glass models. Z. Phys. B, 65(1):53–63, 1986.
    • (1986) Z. Phys. B , vol.65 , Issue.1 , pp. 53-63
    • Van Hemmen, J.L.1    Grensing, D.2    Huber, A.3    Kuhn, R.4
  • 256
    • 0005303790 scopus 로고
    • Sur l’int´egrale de configuration pour les systemes de particules a une dimension
    • L. van Hove. Sur l’int´egrale de configuration pour les systemes de particules a une dimension. Physica, 16:137–43, 1950.
    • (1950) Physica , vol.16 , pp. 137-143
    • Van Hove, L.1
  • 257
    • 0000733381 scopus 로고
    • Fluctuations of extensive functions of quenched random couplings
    • J. Wehr and M. Aizenman. Fluctuations of extensive functions of quenched random couplings. J. Statist. Phys, 60(3–4):287–306, 1990.
    • (1990) J. Statist. Phys , vol.60 , Issue.3-4 , pp. 287-306
    • Wehr, J.1    Aizenman, M.2
  • 258
    • 0000977505 scopus 로고
    • L’hypothese des champ moleculaire et la propri´et´e ferromagn´etique
    • P. Weiss. L’hypothese des champ moleculaire et la propri´et´e ferromagn´etique. J. de Physique, 6:661, 1907.
    • (1907) J. De Physique , vol.6 , pp. 661
    • Weiss, P.1
  • 259
    • 0001136512 scopus 로고
    • On the limit of the largest eigenvalue of the largedimensional sample covariance matrix
    • Y. Q. Yin, Z. D. Bai, and P. R. Krishnaiah. On the limit of the largest eigenvalue of the largedimensional sample covariance matrix. Probab. Theory Related Fields, 78(4):509–21, 1988.
    • (1988) Probab. Theory Related Fields , vol.78 , Issue.4 , pp. 509-521
    • Yin, Y.Q.1    Bai, Z.D.2    Krishnaiah, P.R.3
  • 260
    • 0000836223 scopus 로고
    • Exponential inequalities for sums of random vectors
    • V. V. Yurinski. Exponential inequalities for sums of random vectors. J. Multivariate Anal, 6(4):473–99, 1976.
    • (1976) J. Multivariate Anal , vol.6 , Issue.4 , pp. 473-499
    • Yurinski, V.V.1
  • 261
    • 34250132309 scopus 로고
    • An alternate version of Pirogov–Sinai theory
    • M. Zahradnýk. An alternate version of Pirogov–Sinai theory. Comm. Math. Phys, 93(4):559–81, 1984.
    • (1984) Comm. Math. Phys , vol.93 , Issue.4 , pp. 559-581
    • Zahradnýk, M.1
  • 262
    • 0001714789 scopus 로고    scopus 로고
    • A short course on the Pirogov–Sinai theory
    • M. Zahradnýk. A short course on the Pirogov–Sinai theory. Rend. Mat. Appl. (7), 18(3):411–486, 1998.
    • (1998) Rend. Mat. Appl , vol.18 , Issue.3 , pp. 411-486
    • Zahradnýk, M.1
  • 263
    • 0039359799 scopus 로고    scopus 로고
    • Random spin systems with long-range interactions
    • Boston, MA: Birkh¨auser Boston
    • B. Zegarlinski. Random spin systems with long-range interactions. In Mathematical Aspects of Spin Glasses and Neural Networks, vol. 41 of Progr. Probab, pp. 289–320. Boston, MA: Birkh¨auser Boston, 1998.
    • (1998) Mathematical Aspects of Spin Glasses and Neural Networks , vol.41 , pp. 289-320
    • Zegarlinski, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.