메뉴 건너뛰기




Volumn 119, Issue 1, 2001, Pages 1-30

Weakly Gibbsian representations for joint measures of quenched lattice spin models

Author keywords

Dilute ising model; Disordered systems; Gibbs measures; Ising model; Non Gibbsian measures; Random bond model; Random field model

Indexed keywords


EID: 0035624973     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00012737     Document Type: Article
Times cited : (17)

References (40)
  • 1
    • 11744381258 scopus 로고
    • Rounding effects of quenched randomness on first-order phase transitions
    • Aizenman, M., Wehr, J.: Rounding Effects of Quenched Randomness on First-Order Phase Transitions, Comm. Math. Phys., 130, 489-528 (1990)
    • (1990) Comm. Math. Phys. , vol.130 , pp. 489-528
    • Aizenman, M.1    Wehr, J.2
  • 2
    • 0000702675 scopus 로고
    • Phase transition in the 3d random field ising model
    • Bricmont, J., Kupiainen, A.: Phase transition in the 3d random field Ising model, Comm. Math. Phys., 142, 539-572 (1988)
    • (1988) Comm. Math. Phys. , vol.142 , pp. 539-572
    • Bricmont, J.1    Kupiainen, A.2
  • 3
    • 0032094628 scopus 로고    scopus 로고
    • Renormalization group pathologies and the definition of Gibbs States
    • Bricmont, J., Kupiainen, A., Lefevere, R.: Renormalization Group Pathologies and the Definition of Gibbs States, Comm. Math. Phys., 194, 2, 359-388 (1998)
    • (1998) Comm. Math. Phys. , vol.194 , Issue.2 , pp. 359-388
    • Bricmont, J.1    Kupiainen, A.2    Lefevere, R.3
  • 4
    • 0000178537 scopus 로고
    • A rigorous renormalization group method for interfaces in random media
    • Bovier, A., Külske, C.: A rigorous renormalization group method for interfaces in random media, Rev. Math. Phys., 6(3), 413-496 (1994)
    • (1994) Rev. Math. Phys. , vol.6 , Issue.3 , pp. 413-496
    • Bovier, A.1    Külske, C.2
  • 5
    • 0040750176 scopus 로고    scopus 로고
    • There are no nice interfaces in 2 + 1 dimensional SOS-models in random media
    • Bovier, A., Külske, C.: There are no nice interfaces in 2 + 1 dimensional SOS-models in random media, J. Stat. Phys., 83, 751-759 (1996)
    • (1996) J. Stat. Phys. , vol.83 , pp. 751-759
    • Bovier, A.1    Külske, C.2
  • 6
    • 0004179050 scopus 로고
    • Birkhäuser, Boston, Basel, Stuttgart
    • Cohn, D.L.: Measure Theory, Birkhäuser, Boston, Basel, Stuttgart (1980)
    • (1980) Measure Theory
    • Cohn, D.L.1
  • 7
    • 0001722765 scopus 로고
    • Gibbs states describing a coexistence of phases for the three-dimensional Ising model
    • Dobrushin, R.L.: Gibbs states describing a coexistence of phases for the three-dimensional Ising model, Th. Prob. and its Appl., 17, 582-600 (1972)
    • (1972) Th. Prob. and Its Appl. , vol.17 , pp. 582-600
    • Dobrushin, R.L.1
  • 9
    • 0033466556 scopus 로고    scopus 로고
    • "Non-Gibbsian" states and their Gibbs description
    • Dobrushin, R.L., Shlosman, S.B.: "Non-Gibbsian" states and their Gibbs description, Comm. Math. Phys., 200(1), 125-179 (1999)
    • (1999) Comm. Math. Phys. , vol.200 , Issue.1 , pp. 125-179
    • Dobrushin, R.L.1    Shlosman, S.B.2
  • 10
    • 0007093050 scopus 로고    scopus 로고
    • The renormalization-group peculiarities of griffiths and pearce: What have we learned?
    • Eds Miracle-Solé, S., Ruiz, J. and Zagrebnov, V. Marseille World Scientific
    • van Enter, A.C.D.: The Renormalization-Group peculiarities of Griffiths and Pearce: What have we learned? in: Mathematical Results in Statistical Mechanics, Eds Miracle-Solé, S., Ruiz, J. and Zagrebnov, V. (Marseille 1998), World Scientific 1999, pp. 509-526, also available as preprint 98-692 at http://www.ma.utexas.edu/mp_arc
    • (1998) Mathematical Results in Statistical Mechanics , pp. 509-526
    • Van Enter, A.C.D.1
  • 11
    • 0032137506 scopus 로고    scopus 로고
    • Almost Gibbsian description of the sign fields of SOS fields
    • van Enter, A.C.D., Shlosman, S.B.: (Almost) Gibbsian description of the sign fields of SOS fields, J. Stat. Phys., 92(3-4), 353-368 (1998)
    • (1998) J. Stat. Phys. , vol.92 , Issue.3-4 , pp. 353-368
    • Van Enter, A.C.D.1    Shlosman, S.B.2
  • 12
    • 34250084304 scopus 로고
    • Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
    • van Enter, A.C.D., Fernández, R., Sokal, A.: Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory, J. Stat. Phys., 72, 879-1167 (1993)
    • (1993) J. Stat. Phys. , vol.72 , pp. 879-1167
    • Van Enter, A.C.D.1    Fernández, R.2    Sokal, A.3
  • 14
    • 0007042778 scopus 로고    scopus 로고
    • Measures for lattice systems
    • Invited papers from Statphys 20, Paris
    • Fernandez, R.: Measures for lattice systems, Physica A, 263 (Invited papers from Statphys 20, Paris (1998)), 117-130 (1999), also available as preprint 98-567 at http://www.ma.utexas.edu/mp_arc
    • (1998) Physica A , vol.263 , pp. 117-130
    • Fernandez, R.1
  • 15
    • 0003271843 scopus 로고
    • Gibbs measures and phase transitions
    • de Gruyter, Berlin, New York
    • Georgii. H.O.: Gibbs measures and phase transitions, Studies in mathematics, vol. 9 (de Gruyter, Berlin, New York, 1988)
    • (1988) Studies in Mathematics , vol.9
    • Georgii, H.O.1
  • 16
    • 0014667053 scopus 로고
    • Non-analytic behavior above the critical point in a random Ising ferromagnet
    • Griffiths, R.B.: Non-analytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett., 23, 17-20 (1969)
    • (1969) Phys. Rev. Lett. , vol.23 , pp. 17-20
    • Griffiths, R.B.1
  • 17
    • 0003603239 scopus 로고
    • Convexity in the theory of lattice gases
    • Princeton University Press, Princeton, N.J.
    • Israel, R.B.: Convexity in the theory of lattice gases, Princeton Series in Physics, Princeton University Press, Princeton, N.J. (1979)
    • (1979) Princeton Series in Physics
    • Israel, R.B.1
  • 18
    • 85037257195 scopus 로고
    • Ph.D. Thesis, Ruhr-Universität Bochum
    • Külske, C.: Ph.D. Thesis, Ruhr-Universität Bochum (1993)
    • (1993)
    • Külske, C.1
  • 19
    • 0040453759 scopus 로고    scopus 로고
    • Metastates in disordered mean-field models: Random field and hopfield models
    • Külske, C.: Metastates in Disordered Mean-Field Models: Random Field and Hopfield Models, J. Stat. Phys., 88(5/6), 1257-1293 (1997)
    • (1997) J. Stat. Phys. , vol.88 , Issue.5-6 , pp. 1257-1293
    • Külske, C.1
  • 20
    • 4244134163 scopus 로고    scopus 로고
    • Limiting behavior of random Gibbs measures: Metastates in some disordered mean field models
    • eds. Bovier, A., Picco, P. Birkhäuser Boston, Boston
    • Külske, C.: Limiting behavior of random Gibbs measures: metastates in some disordered mean field models, in: Mathematical aspects of spin glasses and neural networks, Progr. Probab., 41, 151-160 eds. Bovier, A., Picco, P. Birkhäuser Boston, Boston (1998)
    • (1998) Mathematical Aspects of Spin Glasses and Neural Networks, Progr. Probab. , vol.41 , pp. 151-160
    • Külske, C.1
  • 21
    • 0032045210 scopus 로고    scopus 로고
    • Metastates in disordered mean-field models II: The superstates
    • Külske, C.: Metastates in Disordered Mean-Field Models II: The Superstates, J. Stat. Phys., 91(1/2), 155-176 (1998)
    • (1998) J. Stat. Phys. , vol.91 , Issue.1-2 , pp. 155-176
    • Külske, C.1
  • 22
    • 0039528924 scopus 로고    scopus 로고
    • A random energy model for size dependence: Recurrence vs. transience
    • Külske, C.: A random energy model for size dependence: recurrence vs. transience, Prob. Theor. Rel. Fields., 111, 57-100 (1998)
    • (1998) Prob. Theor. Rel. Fields. , vol.111 , pp. 57-100
    • Külske, C.1
  • 23
    • 0007131312 scopus 로고    scopus 로고
    • Non- Gibbsianness and phase transitions in random lattice spin models
    • preprint 99-119 (1999)
    • Külske, C.: (Non-) Gibbsianness and phase transitions in random lattice spin models, Mark. Proc. Rel. Fields., 5, 357-383 (1999) preprint available at http://www.ma.utexas.edu/mp_arc/, preprint 99-119 (1999)
    • (1999) Mark. Proc. Rel. Fields , vol.5 , pp. 357-383
    • Külske, C.1
  • 24
    • 4243259994 scopus 로고
    • Critical behavior of the randomly spin diluted 2D ising model: A grand ensemble approach
    • Kühn, R.: Critical Behavior of the Randomly Spin Diluted 2D Ising Model: A Grand ensemble Approach, Phys. Rev. Lett., 73, No 16, 2268 (1994)
    • (1994) Phys. Rev. Lett. , vol.73 , Issue.16 , pp. 2268
    • Kühn, R.1
  • 25
    • 0002082735 scopus 로고    scopus 로고
    • Equilibrium ensemble approach to disordered systems I: General theory, exact results
    • Kühn, R.: Equilibrium ensemble Approach to Disordered Systems I: General Theory, Exact Results, Z. Phys., B 100, 231-242 (1996)
    • (1996) Z. Phys. , vol.100 B , pp. 231-242
    • Kühn, R.1
  • 26
    • 0016078912 scopus 로고
    • Gibbs description of a system of random variables
    • Kozlov, O.K.: Gibbs Description of a system of random variables, Problems Inform. Transmission., 10, 258-265 (1974)
    • (1974) Problems Inform. Transmission , vol.10 , pp. 258-265
    • Kozlov, O.K.1
  • 27
    • 0033130270 scopus 로고    scopus 로고
    • Weakly Gibbsian measures and quasilocality: A long-range pair-interaction counterexample
    • Lefevere, R.: Weakly Gibbsian measures and quasilocality: a long-range pair-interaction counterexample, J. Stat. Phys., 95 3/4, 785-789 (1999)
    • (1999) J. Stat. Phys. , vol.95 , Issue.3-4 , pp. 785-789
    • Lefevere, R.1
  • 28
    • 0000967134 scopus 로고    scopus 로고
    • Critical behaviour of the 2d spin diluted ising model via the equilibrium ensemble approach
    • Mazzeo, G., Kühn, R.: Critical behaviour of the 2d spin diluted Ising model via the equilibrium ensemble approach, Phys. Rev. E., 60(4), 3823-3836 (1999)
    • (1999) Phys. Rev. E. , vol.60 , Issue.4 , pp. 3823-3836
    • Mazzeo, G.1    Kühn, R.2
  • 29
    • 0242373810 scopus 로고
    • Statistical mechanics of quenched solid solutions with application to magnetically dilute alloys
    • Morita, T.: Statistical mechanics of quenched solid solutions with application to magnetically dilute alloys, J. Math. Phys., 5, 1401-1405 (1964)
    • (1964) J. Math. Phys. , vol.5 , pp. 1401-1405
    • Morita, T.1
  • 30
    • 0002358783 scopus 로고    scopus 로고
    • Almost Gibbsian versus weakly Gibbsian measures
    • preprint 98-193. Erratum, to appear in Stoch. Proc. Appl.
    • Maes, C., Redig, F., Van Moffaert, A.: Almost Gibbsian versus Weakly Gibbsian measures, Stoch.Proc.Appl., 79(1) 1, 1-15 (1999), also available at http://www.ma.utexas.edu/mp_arc/, preprint 98-193. Erratum, to appear in Stoch. Proc. Appl.
    • (1999) Stoch.Proc.Appl. , vol.79 , Issue.1 , pp. 1
    • Maes, C.1    Redig, F.2    Van Moffaert, A.3
  • 31
    • 0034340702 scopus 로고    scopus 로고
    • Percolation, path large deviations and weak Gibbsianity
    • Maes, C., Redig, F., Shlosman, S., Van Moffaert, A.: Percolation, Path Large Deviations and Weak Gibbsianity, Comm. Math. Phys. 209, no. 2, 517-545 (2000)
    • (2000) Comm. Math. Phys. , vol.209 , Issue.2 , pp. 517-545
    • Maes, C.1    Redig, F.2    Shlosman, S.3    Van Moffaert, A.4
  • 33
    • 4243423843 scopus 로고    scopus 로고
    • Spatial inhomogeneity and thermodynamic chaos
    • Newman, C.M., Stein, D.L.: Spatial Inhomogeneity and thermodynamic chaos, Phys. Rev. Lett., 76, No 25, 4821 (1996)
    • (1996) Phys. Rev. Lett. , vol.76 , Issue.25 , pp. 4821
    • Newman, C.M.1    Stein, D.L.2
  • 34
    • 0000003114 scopus 로고    scopus 로고
    • Metastate approach to thermodynamic chaos
    • Newman, C.M., Stein, D.L.: Metastate approach to thermodynamic chaos., Phys. Rev. E., 3, 55, no. 5, part A, 5194-5211 (1997)
    • (1997) Phys. Rev. E. , vol.3-55 , Issue.5 PART A , pp. 5194-5211
    • Newman, C.M.1    Stein, D.L.2
  • 35
    • 4244055093 scopus 로고    scopus 로고
    • Simplicity of state and overlap structure in finite-volume realistic spin glasses
    • Newman, C.M., Stein, D.L.: Simplicity of state and overlap structure in finite-volume realistic spin glasses, Phys. Rev. E, 3, 57, no. 2, part A, 1356-1366 (1998)
    • (1998) Phys. Rev. E , vol.3-57 , Issue.2 PART A , pp. 1356-1366
    • Newman, C.M.1    Stein, D.L.2
  • 36
    • 0007010715 scopus 로고    scopus 로고
    • Thermodynamic chaos and the structure of short-range spin glasses
    • Mathematical aspects of spin glasses and neural networks, Bovier, Picco (Eds.), Birkhäuser, Boston, Boston, MA
    • Newman, C.M., Stein, D.L.: Thermodynamic chaos and the structure of short-range spin glasses, in: Mathematical aspects of spin glasses and neural networks, 243-287, Progr. Probab., 41, Bovier, Picco (Eds.), Birkhäuser, Boston, Boston, MA (1998)
    • (1998) Progr. Probab. , vol.41 , pp. 243-287
    • Newman, C.M.1    Stein, D.L.2
  • 37
    • 0001944670 scopus 로고
    • Projections of Gibbs measures may be non-Gibbsian
    • Schonmann, R.H.: Projections of Gibbs measures may be non-Gibbsian, Comm. Math. Phys., 124, 1-7 (1989)
    • (1989) Comm. Math. Phys. , vol.124 , pp. 1-7
    • Schonmann, R.H.1
  • 38
    • 21844525446 scopus 로고
    • Entropy, limit theorems, and variational principles for disordered lattice systems
    • Seppäläinen, T.: Entropy, limit theorems, and variational principles for disordered lattice systems, Commun. Math. Phys, 171, 233-277 (1995)
    • (1995) Commun. Math. Phys , vol.171 , pp. 233-277
    • Seppäläinen, T.1
  • 39
    • 0001964043 scopus 로고
    • Potentials for almost Markovian random fields
    • Sullivan, W.G.: Potentials for almost Markovian Random Fields, Comm. Math. Phys., 33, 61-74 (1973)
    • (1973) Comm. Math. Phys. , vol.33 , pp. 61-74
    • Sullivan, W.G.1
  • 40
    • 0038993435 scopus 로고
    • Comment on the statistical mechanics of quenched random systems
    • Sobotta, G., Wagner, D.: Comment on the statistical mechanics of quenched random systems, Z. Phys. B. 33(3), 271-274 (1979)
    • (1979) Z. Phys. B. , vol.33 , Issue.3 , pp. 271-274
    • Sobotta, G.1    Wagner, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.