메뉴 건너뛰기




Volumn 348, Issue 1-2, 2001, Pages 5-31

Renormalizing the renormalization group pathologies

Author keywords

Gibbs states; Lattice spin systems; Phase transitions

Indexed keywords


EID: 0008853445     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(00)00134-4     Document Type: Review
Times cited : (12)

References (98)
  • 1
    • 0039875740 scopus 로고
    • Renormalization Group approach to lattice gauge field theories
    • T. Balaban, Renormalization Group approach to lattice gauge field theories, Commun. Math. Phys. 109 (1987) 249-301; 116 (1988) 1-22.
    • (1987) Commun. Math. Phys. , vol.109 , pp. 249-301
    • Balaban, T.1
  • 2
    • 0039875740 scopus 로고
    • T. Balaban, Renormalization Group approach to lattice gauge field theories, Commun. Math. Phys. 109 (1987) 249-301; 116 (1988) 1-22.
    • (1988) Commun. Math. Phys. , vol.116 , pp. 1-22
  • 3
    • 0009396058 scopus 로고
    • A low temperature expansion in classical N-vector models
    • T. Balaban, A low temperature expansion in classical N-vector models, Commun. Math. Phys. 167 (1995) 103-154.
    • (1995) Commun. Math. Phys. , vol.167 , pp. 103-154
    • Balaban, T.1
  • 4
    • 21844517923 scopus 로고
    • Some numerical results on the block spin transformation for the 2d Ising model at the critical point
    • G. Benfatto, E. Marinari, E. Olivieri, Some numerical results on the block spin transformation for the 2d Ising model at the critical point, J. Stat. Phys. 78 (1995) 731-757.
    • (1995) J. Stat. Phys. , vol.78 , pp. 731-757
    • Benfatto, G.1    Marinari, E.2    Olivieri, E.3
  • 5
    • 0003311550 scopus 로고
    • Renormalization Group
    • Princeton University Press, Princeton
    • G. Benfatto, G. Gallavotti, in: Renormalization Group, Physics Notes, Princeton University Press, Princeton, 1995.
    • (1995) Physics Notes
    • Benfatto, G.1    Gallavotti, G.2
  • 6
    • 0033236867 scopus 로고    scopus 로고
    • Renormalization-group transformations under strong mixing conditions: Gibsianness and convergence of renormalized interactions
    • L. Bertini, E. Cirillo, E. Olivieri, Renormalization-group transformations under strong mixing conditions: Gibsianness and convergence of renormalized interactions, J. Stat. Phys. 97 (1999) 831-915.
    • (1999) J. Stat. Phys. , vol.97 , pp. 831-915
    • Bertini, L.1    Cirillo, E.2    Olivieri, E.3
  • 7
    • 0000969121 scopus 로고
    • A unified approach to phase diagrams in field theory and statistical mechanics
    • C. Borgs, J. Imbrie, A unified approach to phase diagrams in field theory and statistical mechanics, Commun. Math. Phys. 123 (1989) 305-328.
    • (1989) Commun. Math. Phys. , vol.123 , pp. 305-328
    • Borgs, C.1    Imbrie, J.2
  • 8
    • 0000702675 scopus 로고
    • Phase transition in the 3d random field Ising model
    • J. Bricmont, A. Kupiainen, Phase transition in the 3d random field Ising model, Commun. Math. Phys. 116 (1988) 539-572.
    • (1988) Commun. Math. Phys. , vol.116 , pp. 539-572
    • Bricmont, J.1    Kupiainen, A.2
  • 9
    • 0009060463 scopus 로고
    • Randoms walks in asymmetric random environments
    • J. Bricmont, A. Kupiainen, Randoms walks in asymmetric random environments, Commun. Math. Phys. 142 (1991) 345-420.
    • (1991) Commun. Math. Phys. , vol.142 , pp. 345-420
    • Bricmont, J.1    Kupiainen, A.2
  • 10
    • 84990739185 scopus 로고
    • Renormalization group and asymptotics of solutions of nonlinear parabolic equations
    • J. Bricmont, A. Kupiainen, G. Lin, Renormalization group and asymptotics of solutions of nonlinear parabolic equations, Commun. Pure Appl. Math. 47 (1994) 893-922.
    • (1994) Commun. Pure Appl. Math. , vol.47 , pp. 893-922
    • Bricmont, J.1    Kupiainen, A.2    Lin, G.3
  • 11
    • 0012165145 scopus 로고
    • Renormalizing partial differential equations
    • V. Rivasseau (Ed.), Constructive Physics, Proceedings, Palaiseau, France, 1994, Springer, Berlin
    • J. Bricmont, A. Kupiainen, Renormalizing partial differential equations, in: V. Rivasseau (Ed.), Constructive Physics, Proceedings, Palaiseau, France, 1994, Lecture Notes in Physics, Springer, Berlin, 1995, pp. 83-115.
    • (1995) Lecture Notes in Physics , pp. 83-115
    • Bricmont, J.1    Kupiainen, A.2
  • 12
    • 0032094628 scopus 로고    scopus 로고
    • Renormalization group pathologies and the definition of Gibbs states
    • J. Bricmont, A. Kupiainen, R. Lefevere, Renormalization group pathologies and the definition of Gibbs states, Commun. Math. Phys. 194 (1998) 359-388.
    • (1998) Commun. Math. Phys. , vol.194 , pp. 359-388
    • Bricmont, J.1    Kupiainen, A.2    Lefevere, R.3
  • 13
    • 0002453502 scopus 로고
    • Phase transitions for systems with a finite number of dominant ground states
    • J. Bricmont, J. Slawny, Phase transitions for systems with a finite number of dominant ground states, J. Stat. Phys. 54 (1989) 89-161.
    • (1989) J. Stat. Phys. , vol.54 , pp. 89-161
    • Bricmont, J.1    Slawny, J.2
  • 15
    • 0001105016 scopus 로고
    • Constructing the three dimensional Gross-Neveu model with a large number of flavor components
    • C. de Calan, P.A. Feria da Veiga, J. Magnen, R. Sénéor, Constructing the three dimensional Gross-Neveu model with a large number of flavor components, Phys. Rev. Lett. 66 (1991) 3233-3236.
    • (1991) Phys. Rev. Lett. , vol.66 , pp. 3233-3236
    • De Calan, C.1    Feria Da Veiga, P.A.2    Magnen, J.3    Sénéor, R.4
  • 16
    • 51249176008 scopus 로고
    • The large block spin interaction
    • C. Cammarota, The large block spin interaction, Il Nuovo Cimento 96B (1986) 1-16.
    • (1986) Il Nuovo Cimento , vol.96 B , pp. 1-16
    • Cammarota, C.1
  • 17
    • 51249189278 scopus 로고
    • The Lavoisier law and the critical point
    • M. Cassandro, G. Gallavotti, The Lavoisier law and the critical point, Il Nuovo Cimento 25B (1975) 695-705.
    • (1975) Il Nuovo Cimento , vol.25 B , pp. 695-705
    • Cassandro, M.1    Gallavotti, G.2
  • 18
    • 0031091664 scopus 로고    scopus 로고
    • Renormalization-group at criticality and complete analyticity of constrained models: A numerical study
    • E. Cirillo, E. Olivieri, Renormalization-group at criticality and complete analyticity of constrained models: a numerical study, J. Stat. Phys. 86 (1997) 1117-1151.
    • (1997) J. Stat. Phys. , vol.86 , pp. 1117-1151
    • Cirillo, E.1    Olivieri, E.2
  • 19
    • 0001722765 scopus 로고
    • Gibbs states describing a coexistence of phases for the three-dimensional Ising model
    • R.L. Dobrushin, Gibbs states describing a coexistence of phases for the three-dimensional Ising model, Theoret. Prob. Appl. 17 (1972) 582-600.
    • (1972) Theoret. Prob. Appl. , vol.17 , pp. 582-600
    • Dobrushin, R.L.1
  • 21
    • 0033466556 scopus 로고    scopus 로고
    • Non-Gibbsian States and their Gibbs description
    • R.L. Dobrushin, S.B. Shlosman, Non-Gibbsian States and their Gibbs description, Commun. Math. Phys. 200 (1999) 125-179.
    • (1999) Commun. Math. Phys. , vol.200 , pp. 125-179
    • Dobrushin, R.L.1    Shlosman, S.B.2
  • 23
    • 0030528480 scopus 로고    scopus 로고
    • Ill-defined block-spin transformations at arbitrarily high temperatures
    • A.C.D. van Enter, Ill-defined block-spin transformations at arbitrarily high temperatures, J. Stat. Phys. 83 (1996) 761-765.
    • (1996) J. Stat. Phys. , vol.83 , pp. 761-765
    • Van Enter, A.C.D.1
  • 24
    • 0009301378 scopus 로고
    • Renormalization in the vicinity of first-order phase transitions: What can and cannot go wrong
    • A.C.D. van Enter, R. Fernández, A.D. Sokal, Renormalization in the vicinity of first-order phase transitions: what can and cannot go wrong, Phys. Rev. Lett. 66 (1991) 3253-3256.
    • (1991) Phys. Rev. Lett. , vol.66 , pp. 3253-3256
    • Van Enter, A.C.D.1    Fernández, R.2    Sokal, A.D.3
  • 25
    • 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. Fernández, A.D. Sokal, Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory, J. Stat. Phys. 72 (1993) 879-1167.
    • (1993) J. Stat. Phys. , vol.72 , pp. 879-1167
    • Van Enter, A.C.D.1    Fernández, R.2    Sokal, A.D.3
  • 26
    • 21844516761 scopus 로고
    • Pathological behavior of renormalization group maps at high fields and above the transition temperature
    • A.C.D. van Enter, R. Fernández, R. Kotecký, Pathological behavior of renormalization group maps at high fields and above the transition temperature, J. Stat. Phys. 79 (1995) 969-992.
    • (1995) J. Stat. Phys. , vol.79 , pp. 969-992
    • Van Enter, A.C.D.1    Fernández, R.2    Kotecký, R.3
  • 27
    • 0009229168 scopus 로고    scopus 로고
    • Robustness of the non-Gibbsian property: Some examples
    • A.C.D. van Enter, J. Lörinczi, Robustness of the non-Gibbsian property: some examples, J. Phys. A Math. Gen. 29 (1996) 2465-2473.
    • (1996) J. Phys. A Math. Gen. , vol.29 , pp. 2465-2473
    • Van Enter, A.C.D.1    Lörinczi, J.2
  • 28
    • 0032137506 scopus 로고    scopus 로고
    • (Almost) Gibbsian description of the sign fields of SOS fields
    • A.C.D. van Enter, S. Shlosman, (Almost) Gibbsian description of the sign fields of SOS fields, J. Stat. Phys. 92 (1998) 353-367.
    • (1998) J. Stat. Phys. , vol.92 , pp. 353-367
    • Van Enter, A.C.D.1    Shlosman, S.2
  • 29
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • M. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978) 25-52.
    • (1978) J. Stat. Phys. , vol.19 , pp. 25-52
    • Feigenbaum, M.1
  • 30
    • 0347447535 scopus 로고
    • The universal metric properties of nonlinear transformations
    • M. Feigenbaum, The universal metric properties of nonlinear transformations, J. Stat. Phys. 21 (1979) 669-706.
    • (1979) J. Stat. Phys. , vol.21 , pp. 669-706
    • Feigenbaum, M.1
  • 32
    • 0002546548 scopus 로고
    • A renormalizable field theory: The massive Gross-Neveu model in two dimensions
    • J. Feldman, J. Magnen, V. Rivasseau, R. Sénéor, A renormalizable field theory: the massive Gross-Neveu model in two dimensions, Commun. Math. Phys. 103 (1986) 67-103.
    • (1986) Commun. Math. Phys. , vol.103 , pp. 67-103
    • Feldman, J.1    Magnen, J.2    Rivasseau, V.3    Sénéor, R.4
  • 33
    • 0039644940 scopus 로고    scopus 로고
    • Global specifications and non-quasilocality of projections of Gibbs measures
    • R. Fernández, C.-Ed. Pfister, Global specifications and non-quasilocality of projections of Gibbs measures, Ann. Prob. 25 (1997) 1284-1315.
    • (1997) Ann. Prob. , vol.25 , pp. 1284-1315
    • Fernández, R.1    Pfister, C.-Ed.2
  • 35
    • 0032393880 scopus 로고    scopus 로고
    • Renormalization Group theory: Its basis and formulation in statistical physics
    • M.E. Fisher, Renormalization Group theory: its basis and formulation in statistical physics, Rev. Mod. Phys. 70 (1998) 653-681.
    • (1998) Rev. Mod. Phys. , vol.70 , pp. 653-681
    • Fisher, M.E.1
  • 36
    • 0009207118 scopus 로고
    • Block spins interactions in the Ising model
    • G. Gallavotti, H. Knops, Block spins interactions in the Ising model, Commun. Math. Phys. 36 (1974) 171-184.
    • (1974) Commun. Math. Phys. , vol.36 , pp. 171-184
    • Gallavotti, G.1    Knops, H.2
  • 37
    • 0342346232 scopus 로고
    • Boundary conditions and correlation functions in the v-dimensional Ising model at low temperature
    • G. Gallavotti, Boundary conditions and correlation functions in the v-dimensional Ising model at low temperature, Commun. Math. Phys. 23 (1971) 275-284.
    • (1971) Commun. Math. Phys. , vol.23 , pp. 275-284
    • Gallavotti, G.1
  • 38
    • 0039739101 scopus 로고
    • Block spins distributions for short range attractive Ising models
    • G. Gallavotti, A. Martin-Löf, Block spins distributions for short range attractive Ising models, Il Nuovo Cimento 36 (1974) 1-16.
    • (1974) Il Nuovo Cimento , vol.36 , pp. 1-16
    • Gallavotti, G.1    Martin-Löf, A.2
  • 39
    • 0001629746 scopus 로고
    • Coarse graining approach to first order phase transitions
    • K. Gawȩdzki, R. Kotecký, A. Kupiainen, Coarse graining approach to first order phase transitions, J. Stat. Phys. 47 (1987) 701-724.
    • (1987) J. Stat. Phys. , vol.47 , pp. 701-724
    • Gawȩdzki, K.1    Kotecký, R.2    Kupiainen, A.3
  • 40
    • 35949020391 scopus 로고
    • 4 theory: A non-perturbative control of a renormalizable model
    • 4 theory: a non-perturbative control of a renormalizable model, Phys. Rev. Lett. 54 (1985) 92-95.
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 92-95
    • Gawȩdzki, K.1    Kupiainen, A.2
  • 41
    • 0002590160 scopus 로고
    • Gross-Neveu model through convergent perturbation expansions
    • K. Gawȩdzki, A. Kupiainen, Gross-Neveu model through convergent perturbation expansions, Commun. Math. Phys. 102 (1985) 1-30.
    • (1985) Commun. Math. Phys. , vol.102 , pp. 1-30
    • Gawȩdzki, K.1    Kupiainen, A.2
  • 42
    • 33847349969 scopus 로고
    • Exact renormalization for the Gross-Neveu model of quantum fields
    • K. Gawȩdzki, A. Kupiainen, Exact renormalization for the Gross-Neveu model of quantum fields, Phys. Rev. Lett. 54 (1985) 2191-2194.
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 2191-2194
    • Gawȩdzki, K.1    Kupiainen, A.2
  • 43
    • 34848855197 scopus 로고
    • Renormalizing the non-renormalizable
    • K. Gawȩdzki, A. Kupiainen, Renormalizing the non-renormalizable, Phys. Rev. Lett. 55 (1985) 363-367.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 363-367
    • Gawȩdzki, K.1    Kupiainen, A.2
  • 44
    • 0002120555 scopus 로고
    • Renormalization of a non-renormalizable quantum field theory
    • K. Gawȩdzki, A. Kupiainen, Renormalization of a non-renormalizable quantum field theory, Nucl. Phys. B262 (1985) 33-48.
    • (1985) Nucl. Phys. , vol.B262 , pp. 33-48
    • Gawȩdzki, K.1    Kupiainen, A.2
  • 45
    • 34250115578 scopus 로고
    • 4 theory: Rigorous control of a renormalizable asymptotically free model
    • 4 theory: rigorous control of a renormalizable asymptotically free model, Commun. Math. Phys. 99 (1985) 197-252.
    • (1985) Commun. Math. Phys. , vol.99 , pp. 197-252
    • Gawȩdzki, K.1    Kupiainen, A.2
  • 46
    • 0003271843 scopus 로고
    • Gibbs Measures and Phase Transitions
    • Walter de Gruyter, Berlin, New York
    • H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Studies in Mathematics, Vol. 9, Walter de Gruyter, Berlin, New York, 1988.
    • (1988) de Gruyter Studies in Mathematics , vol.9
    • Georgii, H.-O.1
  • 47
    • 0024795190 scopus 로고
    • Intermediate asymptotics and renormalization group theory
    • N. Goldenfeld, O. Martin, Y. Oono, Intermediate asymptotics and renormalization group theory, J. Sci. Comput. 4 (1989) 355-372; N. Goldenfeld, O. Martin, Y. Oono, F. Liu, Anomalous dimensions and the renormalization group in a nonlinear diffusion process, Phys. Rev. Lett. 64 (1990) 1361-1364: N. Goldenfeld, O. Martin, Y. Oono, Asymptotics of partial differential equations and the renormalization group, in: H. Segur, S. Tanveer, H. Levine (Eds.), Proceedings of the NATO ARW on Asymptotics Beyond all Orders, Plenum Press, New York, 1991; N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics, Vol. 85, Addison-Wesley, Reading, MA, 1992; L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group theory for global asymptotic analysis, Phys. Rev. Lett. 73 (1994) 1311-1315.
    • (1989) J. Sci. Comput. , vol.4 , pp. 355-372
    • Goldenfeld, N.1    Martin, O.2    Oono, Y.3
  • 48
    • 0000062672 scopus 로고
    • Anomalous dimensions and the renormalization group in a nonlinear diffusion process
    • N. Goldenfeld, O. Martin, Y. Oono, Intermediate asymptotics and renormalization group theory, J. Sci. Comput. 4 (1989) 355-372; N. Goldenfeld, O. Martin, Y. Oono, F. Liu, Anomalous dimensions and the renormalization group in a nonlinear diffusion process, Phys. Rev. Lett. 64 (1990) 1361-1364: N. Goldenfeld, O. Martin, Y. Oono, Asymptotics of partial differential equations and the renormalization group, in: H. Segur, S. Tanveer, H. Levine (Eds.), Proceedings of the NATO ARW on Asymptotics Beyond all Orders, Plenum Press, New York, 1991; N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics, Vol. 85, Addison-Wesley, Reading, MA, 1992; L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group theory for global asymptotic analysis, Phys. Rev. Lett. 73 (1994) 1311-1315.
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 1361-1364
    • Goldenfeld, N.1    Martin, O.2    Oono, Y.3    Liu, F.4
  • 49
    • 0024795190 scopus 로고
    • Asymptotics of partial differential equations and the renormalization group
    • H. Segur, S. Tanveer, H. Levine (Eds.), Plenum Press, New York
    • N. Goldenfeld, O. Martin, Y. Oono, Intermediate asymptotics and renormalization group theory, J. Sci. Comput. 4 (1989) 355-372; N. Goldenfeld, O. Martin, Y. Oono, F. Liu, Anomalous dimensions and the renormalization group in a nonlinear diffusion process, Phys. Rev. Lett. 64 (1990) 1361-1364: N. Goldenfeld, O. Martin, Y. Oono, Asymptotics of partial differential equations and the renormalization group, in: H. Segur, S. Tanveer, H. Levine (Eds.), Proceedings of the NATO ARW on Asymptotics Beyond all Orders, Plenum Press, New York, 1991; N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics, Vol. 85, Addison-Wesley, Reading, MA, 1992; L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group theory for global asymptotic analysis, Phys. Rev. Lett. 73 (1994) 1311-1315.
    • (1991) Proceedings of the NATO ARW on Asymptotics Beyond All Orders
    • Goldenfeld, N.1    Martin, O.2    Oono, Y.3
  • 50
    • 0024795190 scopus 로고
    • Lectures on Phase Transitions and the Renormalization Group
    • Addison-Wesley, Reading, MA
    • N. Goldenfeld, O. Martin, Y. Oono, Intermediate asymptotics and renormalization group theory, J. Sci. Comput. 4 (1989) 355-372; N. Goldenfeld, O. Martin, Y. Oono, F. Liu, Anomalous dimensions and the renormalization group in a nonlinear diffusion process, Phys. Rev. Lett. 64 (1990) 1361-1364: N. Goldenfeld, O. Martin, Y. Oono, Asymptotics of partial differential equations and the renormalization group, in: H. Segur, S. Tanveer, H. Levine (Eds.), Proceedings of the NATO ARW on Asymptotics Beyond all Orders, Plenum Press, New York, 1991; N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics, Vol. 85, Addison-Wesley, Reading, MA, 1992; L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group theory for global asymptotic analysis, Phys. Rev. Lett. 73 (1994) 1311-1315.
    • (1992) Frontiers in Physics , vol.85
    • Goldenfeld, N.1
  • 51
    • 0000991711 scopus 로고
    • Renormalization group theory for global asymptotic analysis
    • N. Goldenfeld, O. Martin, Y. Oono, Intermediate asymptotics and renormalization group theory, J. Sci. Comput. 4 (1989) 355-372; N. Goldenfeld, O. Martin, Y. Oono, F. Liu, Anomalous dimensions and the renormalization group in a nonlinear diffusion process, Phys. Rev. Lett. 64 (1990) 1361-1364: N. Goldenfeld, O. Martin, Y. Oono, Asymptotics of partial differential equations and the renormalization group, in: H. Segur, S. Tanveer, H. Levine (Eds.), Proceedings of the NATO ARW on Asymptotics Beyond all Orders, Plenum Press, New York, 1991; N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics, Vol. 85, Addison-Wesley, Reading, MA, 1992; L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group theory for global asymptotic analysis, Phys. Rev. Lett. 73 (1994) 1311-1315.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 1311-1315
    • Chen, L.-Y.1    Goldenfeld, N.2    Oono, Y.3
  • 52
    • 0014667053 scopus 로고
    • Nonanalytic behavior above the critical point in a random Ising ferromagnet
    • R.B. Griffiths, Nonanalytic behavior above the critical point in a random Ising ferromagnet, Phys. Rev. Lett. 23 (1969) 17-20.
    • (1969) Phys. Rev. Lett. , vol.23 , pp. 17-20
    • Griffiths, R.B.1
  • 53
    • 0001766181 scopus 로고
    • Position-space renormalization-group transformations: Some proofs and some problems
    • R.B. Griffiths, P.A. Pearce, Position-space renormalization-group transformations: some proofs and some problems, Phys. Rev. Lett. 41 (1978) 917-920.
    • (1978) Phys. Rev. Lett. , vol.41 , pp. 917-920
    • Griffiths, R.B.1    Pearce, P.A.2
  • 54
    • 0642265805 scopus 로고
    • Mathematical properties of position-space renormalization-group transformations
    • R.B. Griffiths, P.A. Pearce, Mathematical properties of position-space renormalization-group transformations, J. Stat. Phys. 20 (1979) 499-545.
    • (1979) J. Stat. Phys. , vol.20 , pp. 499-545
    • Griffiths, R.B.1    Pearce, P.A.2
  • 55
    • 0030501842 scopus 로고    scopus 로고
    • Absence of renormalization group pathologies near the critical temperature - Two examples
    • K. Haller, T. Kennedy, Absence of renormalization group pathologies near the critical temperature - two examples, J. Stat. Phys. 85 (1996) 607-637.
    • (1996) J. Stat. Phys. , vol.85 , pp. 607-637
    • Haller, K.1    Kennedy, T.2
  • 56
    • 0002566633 scopus 로고
    • Singular renormalization group transformations and first order phase transitions (I)
    • A. Hasenfratz, P. Hasenfratz, Singular renormalization group transformations and first order phase transitions (I), Nucl. Phys. B 295 (FS21) (1988) 1-20.
    • (1988) Nucl. Phys. B , vol.295 , Issue.FS21 , pp. 1-20
    • Hasenfratz, A.1    Hasenfratz, P.2
  • 57
    • 0000721414 scopus 로고
    • The ground state of the three-dimensional random-field Ising model
    • J. Imbrie, The ground state of the three-dimensional random-field Ising model, Commun. Math. Phys. 98 (1985) 145-176.
    • (1985) Commun. Math. Phys. , vol.98 , pp. 145-176
    • Imbrie, J.1
  • 59
    • 0000941582 scopus 로고
    • Random-field instability of the ordered state of continuous symmetry
    • Y. Imry, S.K. Ma, Random-field instability of the ordered state of continuous symmetry, Phys. Rev. Lett. 35 (1975) 1399-1401.
    • (1975) Phys. Rev. Lett. , vol.35 , pp. 1399-1401
    • Imry, Y.1    Ma, S.K.2
  • 61
    • 0001616373 scopus 로고
    • Banach algebras and Kadanoff transformations
    • J. Fritz, L. Lebowitz, D. Szász (Eds.), Esztergom, North-Holland, Amsterdam
    • R.B. Israel, Banach algebras and Kadanoff transformations, in: J. Fritz, L. Lebowitz, D. Szász (Eds.), Random Fields (Esztergom, 1979), Vol. II, North-Holland, Amsterdam, 1981, pp. 593-608.
    • (1979) Random Fields , vol.2 , pp. 593-608
    • Israel, R.B.1
  • 62
    • 21144459110 scopus 로고
    • Some rigorous results on majority rule renormalization group transformations near the critical point
    • T. Kennedy, Some rigorous results on majority rule renormalization group transformations near the critical point, J. Stat. Phys. 72 (1993) 15-37.
    • (1993) J. Stat. Phys. , vol.72 , pp. 15-37
    • Kennedy, T.1
  • 63
    • 0000639657 scopus 로고
    • Cluster expansion for abstract polymer models
    • R. Kotecký, D. Preiss, Cluster expansion for abstract polymer models, Commun. Math. Phys. 103 (1986) 491-498.
    • (1986) Commun. Math. Phys. , vol.103 , pp. 491-498
    • Kotecký, R.1    Preiss, D.2
  • 64
    • 0016078912 scopus 로고
    • Gibbs Description of a system of random variables
    • O.K. Kozlov, Gibbs Description of a system of random variables, Probl. Inform. Transmission 10 (1974) 258-265.
    • (1974) Probl. Inform. Transmission , vol.10 , pp. 258-265
    • Kozlov, O.K.1
  • 65
    • 0007131312 scopus 로고    scopus 로고
    • (Non-)Gibbsianness and phase transitions in random lattice spin models
    • C. Külske, (Non-)Gibbsianness and phase transitions in random lattice spin models, Markov Process. Related Fields 5 (1999) 357-383.
    • (1999) Markov Process. Related Fields , vol.5 , pp. 357-383
    • Külske, C.1
  • 66
    • 0002809224 scopus 로고
    • Almost sure entropy and the variational principle for random fields with unbounded state space
    • H. Künsch, Almost sure entropy and the variational principle for random fields with unbounded state space, Z. Wahrscheinlichkeitstheorie Verw. Geb. 58 (1981) 69-85.
    • (1981) Z. Wahrscheinlichkeitstheorie Verw. Geb. , vol.58 , pp. 69-85
    • Künsch, H.1
  • 67
    • 21044442631 scopus 로고
    • Statistical mechanics of probabilistic cellular automata
    • J.L. Lebowitz, C. Maes, E.R. Speer, Statistical mechanics of probabilistic cellular automata, J. Stat. Phys. 59 (1990) 117-170.
    • (1990) J. Stat. Phys. , vol.59 , pp. 117-170
    • Lebowitz, J.L.1    Maes, C.2    Speer, E.R.3
  • 68
    • 0001763532 scopus 로고
    • Statistical mechanics of systems of unbounded spins
    • J.L. Lebowitz, E. Presutti, Statistical mechanics of systems of unbounded spins, Commun. Math. Phys. 50 (1976) 195-218.
    • (1976) Commun. Math. Phys. , vol.50 , pp. 195-218
    • Lebowitz, J.L.1    Presutti, E.2
  • 69
    • 0033130270 scopus 로고    scopus 로고
    • Weakly Gibbsian measures and quasilocality: A long range pair-interaction counterexample
    • R. Lefevere, Weakly Gibbsian measures and quasilocality: a long range pair-interaction counterexample, J. Stat. Phys. 95 (1999) 789-793.
    • (1999) J. Stat. Phys. , vol.95 , pp. 789-793
    • Lefevere, R.1
  • 70
    • 0033245915 scopus 로고    scopus 로고
    • Variational principle for some renormalized measures
    • R. Lefevere, Variational principle for some renormalized measures, J. Stat. Phys. 96 (1999) 109-134.
    • (1999) J. Stat. Phys. , vol.96 , pp. 109-134
    • Lefevere, R.1
  • 71
    • 0033724876 scopus 로고    scopus 로고
    • A note on the renormalization group and contour expansions
    • R. Lefevere, A note on the renormalization group and contour expansions, Physica A 286 (2000) 599-610.
    • (2000) Physica A , vol.286 , pp. 599-610
    • Lefevere, R.1
  • 72
    • 21844518961 scopus 로고
    • A note on the projection of Gibbs measures
    • J. Lörinczi, K. Vande Velde, A note on the projection of Gibbs measures, J. Stat. Phys. 77 (1994) 881-887.
    • (1994) J. Stat. Phys. , vol.77 , pp. 881-887
    • Lörinczi, J.1    Vande Velde, K.2
  • 73
    • 0040041132 scopus 로고
    • Some results on the projected two-dimensional Ising model
    • M. Fannes, C. Maes, A. Verbeure (Eds.), Plenum Press, New York
    • J. Lörinczi, Some results on the projected two-dimensional Ising model, in: M. Fannes, C. Maes, A. Verbeure (Eds.), Proceedings NATO ASI Workshop "On Three Levels", Plenum Press, New York, 1994, pp. 373-380.
    • (1994) Proceedings NATO ASI Workshop "On Three Levels" , pp. 373-380
    • Lörinczi, J.1
  • 74
    • 0039739102 scopus 로고
    • Some remarks on almost Gibbs states
    • N. Boccara, E. Goles, S. Martinez, P. Picco (Eds.), Kluwer, Dordrecht
    • J. Lörinczi, M. Winnink, Some remarks on almost Gibbs states, in: N. Boccara, E. Goles, S. Martinez, P. Picco (Eds.), Cellular Automata and Cooperative Systems, Kluwer, Dordrecht, 1993, pp. 423-432.
    • (1993) Cellular Automata and Cooperative Systems , pp. 423-432
    • Lörinczi, J.1    Winnink, M.2
  • 75
    • 0009286535 scopus 로고
    • Defining relative energies for the projected Ising measure
    • C. Maes, K. Vande Velde, Defining relative energies for the projected Ising measure, Helv. Phys. Acta 65 (1992) 1055-1068.
    • (1992) Helv. Phys. Acta , vol.65 , pp. 1055-1068
    • Maes, C.1    Vande Velde, K.2
  • 76
    • 43949148896 scopus 로고
    • The (non-)Gibbsian nature of states invariant under stochastic transformations
    • C. Maes, K. Vande Velde, The (non-)Gibbsian nature of states invariant under stochastic transformations, Physica A 206 (1994) 587-603.
    • (1994) Physica A , vol.206 , pp. 587-603
    • Maes, C.1    Vande Velde, K.2
  • 77
    • 0001028722 scopus 로고    scopus 로고
    • Relative energies for non-Gibbsian states
    • C. Maes, K. Vande Velde, Relative energies for non-Gibbsian states, Commun. Math. Phys. 189 (1997) 277-286.
    • (1997) Commun. Math. Phys. , vol.189 , pp. 277-286
    • Maes, C.1    Vande Velde, K.2
  • 81
    • 85087243043 scopus 로고    scopus 로고
    • The restriction of the Ising model to a layer
    • C. Maes, F. Redig, A. Van Moffaert, The restriction of the Ising model to a layer, J. Stat. Phys. 94 (1999) 893-912.
    • (1999) J. Stat. Phys. , vol.94 , pp. 893-912
    • Maes, C.1    Redig, F.2    Van Moffaert, A.3
  • 82
    • 0033273854 scopus 로고    scopus 로고
    • Freezing transition in the Ising model without internal contours
    • C. Maes, S. Shlosman, Freezing transition in the Ising model without internal contours, Prob. Theory Related Fields 115 (1999) 479-503.
    • (1999) Prob. Theory Related Fields , vol.115 , pp. 479-503
    • Maes, C.1    Shlosman, S.2
  • 84
    • 21144472356 scopus 로고
    • 4 with an infrared cutoff
    • 4 with an infrared cutoff, Commun. Math. Phys. 155 (1993) 325-383.
    • (1993) Commun. Math. Phys. , vol.155 , pp. 325-383
  • 85
    • 21144477881 scopus 로고
    • Some remarks on pathologies of renormalization-group transformations
    • F. Martinelli, E. Olivieri, Some remarks on pathologies of renormalization-group transformations, J. Stat. Phys. 72 (1993) 1169-1177.
    • (1993) J. Stat. Phys. , vol.72 , pp. 1169-1177
    • Martinelli, F.1    Olivieri, E.2
  • 86
    • 21844483152 scopus 로고
    • Instability of renormalization-group pathologies under decimation
    • F. Martinelli, E. Olivieri, Instability of renormalization-group pathologies under decimation, J. Stat. Phys. 79 (1995) 25-42.
    • (1995) J. Stat. Phys. , vol.79 , pp. 25-42
    • Martinelli, F.1    Olivieri, E.2
  • 88
    • 0002749724 scopus 로고
    • Phase diagrams of classical spin systems
    • S. Pirogov, Ya. Sinai. Phase diagrams of classical spin systems, Theor. Math. Phys. 25 (1975) 1185-1192, and 26 (1976) 39-49.
    • (1975) Theor. Math. Phys. , vol.25 , pp. 1185-1192
    • Pirogov, S.1    Sinai, Ya.2
  • 89
    • 0002749724 scopus 로고
    • S. Pirogov, Ya. Sinai. Phase diagrams of classical spin systems, Theor. Math. Phys. 25 (1975) 1185-1192, and 26 (1976) 39-49.
    • (1976) Theor. Math. Phys. , vol.26 , pp. 39-49
  • 91
    • 0001944670 scopus 로고
    • Projections of Gibbs measures may be non-Gibbsian
    • R. Schonmann, Projections of Gibbs measures may be non-Gibbsian, Commun. Math. Phys. 124 (1989) 1-7.
    • (1989) Commun. Math. Phys. , vol.124 , pp. 1-7
    • Schonmann, R.1
  • 94
    • 0003267850 scopus 로고
    • Low temperature properties of classical lattice systems: Phase transitions and phase diagrams
    • C. Domb, J.L. Lebowitz (Eds.), Academic Press, New York
    • J. Slawny, Low temperature properties of classical lattice systems: phase transitions and phase diagrams, in: C. Domb, J.L. Lebowitz (Eds.), Phase Transitions and Critical Phenomena, Vol. 11, Academic Press, New York, 1987.
    • (1987) Phase Transitions and Critical Phenomena , vol.11
    • Slawny, J.1
  • 95
    • 0001964043 scopus 로고
    • Potentials for almost Markovian random fields
    • W.G. Sullivan, Potentials for almost Markovian random fields, Commun. Math. Phys. 33 (1973) 61-74.
    • (1973) Commun. Math. Phys. , vol.33 , pp. 61-74
    • Sullivan, W.G.1
  • 96
    • 34250132309 scopus 로고
    • An alternative version of Pirogov-Sinai theory
    • M. Zahradnik, An alternative version of Pirogov-Sinai theory, Commun. Math. Phys. 93 (1984) 559-581.
    • (1984) Commun. Math. Phys. , vol.93 , pp. 559-581
    • Zahradnik, M.1
  • 97
    • 0000334559 scopus 로고    scopus 로고
    • Problems with the definition of renormalized Hamiltonians for the momentum-space renormalization transformations
    • A.C.D. van Enter, R. Fernández, Problems with the definition of renormalized Hamiltonians for the momentum-space renormalization transformations, Phys. Rev. E 59 (1999) 5165-5171.
    • (1999) Phys. Rev. E , vol.59 , pp. 5165-5171
    • Van Enter, A.C.D.1    Fernández, R.2
  • 98
    • 0346705146 scopus 로고    scopus 로고
    • The Griffiths singularity random field. On Dobrushin's way. From probability theory to statistical physics
    • American Mathematical Society, Providence RI
    • A.C.D. van Enter, C. Maes, R.H. Schonmann, S. Shlosman, The Griffiths singularity random field. On Dobrushin's way. From probability theory to statistical physics, Amer. Math. Soc. Transl. Ser. 2, Vol. 298, American Mathematical Society, Providence RI, 2000, pp. 51-58.
    • (2000) Amer. Math. Soc. Transl. Ser. 2 , vol.298 , pp. 51-58
    • Van Enter, A.C.D.1    Maes, C.2    Schonmann, R.H.3    Shlosman, S.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.