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Volumn 86, Issue 5-6, 1997, Pages 1117-1151

Renormalization group at criticality and complete analyticity of constrained models: A numerical study

Author keywords

Complete analyticity; Finite size conditions; Ising model; Majority rule; Non Gibbsianness; Renormalization group

Indexed keywords


EID: 0031091664     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02183617     Document Type: Article
Times cited : (6)

References (37)
  • 1
    • 21844517923 scopus 로고
    • Some numerical results on the block spin transformation for the 2D ising model at the critical point
    • G. Benfatto, E. Marinari, and H. Olivieri, Some numerical results on the block spin transformation for the 2D Ising model at the critical point, J. Stat. Phys. 78:731-757 (1995).
    • (1995) J. Stat. Phys. , vol.78 , pp. 731-757
    • Benfatto, G.1    Marinari, E.2    Olivieri, H.3
  • 2
    • 51249176008 scopus 로고
    • The large block spin interaction
    • C. Cammarota, The large block spin interaction. Nuovo Cimento 96B:1-16 (1986).
    • (1986) Nuovo Cimento , vol.96 B , pp. 1-16
    • Cammarota, C.1
  • 3
    • 51249189278 scopus 로고
    • The Lavoisier law and the critical point
    • M. Cassandro and G. Gallavotti, The Lavoisier law and the critical point, Nuovo Cimento 25B:691 (1975).
    • (1975) Nuovo Cimento , vol.25 B , pp. 691
    • Cassandro, M.1    Gallavotti, G.2
  • 4
    • 0000080779 scopus 로고
    • Prescribing a system of random variables by conditional distributions
    • R. L. Dobrushin, Prescribing a system of random variables by conditional distributions, Theory Prob. Appl. 15:453-486 (1970).
    • (1970) Theory Prob. Appl. , vol.15 , pp. 453-486
    • Dobrushin, R.L.1
  • 5
    • 0009125823 scopus 로고
    • Lecture given at the workshop
    • Renkum, Holland
    • R. L. Dobrushin, Lecture given at the workshop, Probability and Physics, Renkum, Holland (1995).
    • (1995) Probability and Physics
    • Dobrushin, R.L.1
  • 8
    • 0001217140 scopus 로고
    • Completely analytical interactions constructive description
    • R. L. Dobrushin and S. Shlosman, Completely analytical interactions constructive description, J. Stat. Phys. 46:983-1014 (1987).
    • (1987) J. Stat. Phys. , vol.46 , pp. 983-1014
    • Dobrushin, R.L.1    Shlosman, S.2
  • 9
    • 0030528480 scopus 로고    scopus 로고
    • III-defined block-spin transformations at arbitrarily high temperatures
    • A. C. D. van Enter, III-defined block-spin transformations at arbitrarily high temperatures, J. Stat. Phys. 83:761-765 (1996).
    • (1996) J. Stat. Phys. , vol.83 , pp. 761-765
    • Van Enter, A.C.D.1
  • 11
    • 21844516761 scopus 로고
    • Pathological behavior of renormalization group maps at high field and above the transition temperature
    • A. C. D. van Enter, R. Fernández, and R. Kotecký, Pathological behavior of renormalization group maps at high field and above the transition temperature, J. Stat. Phys. 79:969-992 (1995).
    • (1995) J. Stat. Phys. , vol.79 , pp. 969-992
    • Van Enter, A.C.D.1    Fernández, R.2    Kotecký, R.3
  • 12
    • 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, and A. D. Sokal, Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory, J. Stat. Phys. 72:879-1167 (1994).
    • (1994) J. Stat. Phys. , vol.72 , pp. 879-1167
    • Van Enter, A.C.D.1    Fernández, R.2    Sokal, A.D.3
  • 14
    • 0642265805 scopus 로고
    • Mathematical properties of position-space renormalization group transformations
    • R. B. Griffiths and P. A. Pearce, Mathematical properties of position-space renormalization group transformations, J. Stat. Phys. 20:499-545 (1979).
    • (1979) J. Stat. Phys. , vol.20 , pp. 499-545
    • Griffiths, R.B.1    Pearce, P.A.2
  • 16
    • 0001616373 scopus 로고
    • Banach algebras and Kadanoff transformations
    • J. Fritz, J. L. Lebowitz, and D. Szasz, eds. North-Holland, Amsterdam
    • R. B. Israel, Banach algebras and Kadanoff transformations, in Random Fields, Vol. II, pp. 593-608, J. Fritz, J. L. Lebowitz, and D. Szasz, eds. (North-Holland, Amsterdam, 1981).
    • (1981) Random Fields , vol.2 , pp. 593-608
    • Israel, R.B.1
  • 17
    • 0030544742 scopus 로고    scopus 로고
    • Extended application of high noise constructive criteria for ergodicity of interacting particle systems
    • H. de Jong and Ch. Maes, Extended application of high noise constructive criteria for ergodicity of interacting particle systems. Int. J. Mol. Phys. C 7:1-18 (1996).
    • (1996) Int. J. Mol. Phys. C , vol.7 , pp. 1-18
    • De Jong, H.1    Maes, Ch.2
  • 18
    • 0040591969 scopus 로고
    • A fixed point equation for the high temperature phase of discrete lattice spin systems
    • T. Kennedy, A fixed point equation for the high temperature phase of discrete lattice spin systems, J. Stat. Phys. 59:195 (1990).
    • (1990) J. Stat. Phys. , vol.59 , pp. 195
    • Kennedy, T.1
  • 19
    • 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. 72:15 (1993).
    • (1993) J. Stat. Phys. , vol.72 , pp. 15
    • Kennedy, T.1
  • 20
    • 0039998835 scopus 로고    scopus 로고
    • Private communication
    • T. Kennedy, Private communication.
    • Kennedy, T.1
  • 21
    • 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 10:258-265 (1974).
    • (1974) Probl. Inform. Transmission , vol.10 , pp. 258-265
    • Kozlov, O.K.1
  • 23
    • 21844518961 scopus 로고
    • A note on the projection of Gibbs measures
    • J. Lorinczi, and K. Vande Velde, A note on the projection of Gibbs measures, J. Stat. Phys. 77:881-887 (1994).
    • (1994) J. Stat. Phys. , vol.77 , pp. 881-887
    • Lorinczi, J.1    Velde, K.V.2
  • 24
    • 0041186044 scopus 로고    scopus 로고
    • Private communication
    • Ch. Maes, Private communication.
    • Maes, Ch.1
  • 25
    • 0039041413 scopus 로고
    • Coupling interacting particle systems
    • Ch. Maes, Coupling interacting particle systems. Rev. Math. Phys. 5:457-475 (1995).
    • (1995) Rev. Math. Phys. , vol.5 , pp. 457-475
    • Maes, Ch.1
  • 26
    • 0009285723 scopus 로고
    • Finite volume mixing conditions for lattice spin systems and exponential approach to equilibrium of Glauber dynamics
    • N. Boccara, E. Goles, S. Martinez, and P. Picco, eds. Kluwer, Dordrecht
    • F. Martinelli and E. Olivieri, Finite volume mixing conditions for lattice spin systems and exponential approach to equilibrium of Glauber dynamics, in Proceedings of 1992 Les Hauches Conference on Cellular Automata and Cooperative Systems, N. Boccara, E. Goles, S. Martinez, and P. Picco, eds. (Kluwer, Dordrecht, 1993).
    • (1993) Proceedings of 1992 Les Hauches Conference on Cellular Automata and Cooperative Systems
    • Martinelli, F.1    Olivieri, E.2
  • 27
    • 34249767236 scopus 로고
    • Approach to equilibrium of Glauber dynamics in the one phase region I. The attractive case
    • F. Maninelli and E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region I. The attractive case, Commun. Math. Phys. 161:447-486 (1994).
    • (1994) Commun. Math. Phys. , vol.161 , pp. 447-486
    • Maninelli, F.1    Olivieri, E.2
  • 28
    • 21344495138 scopus 로고
    • Approach to equilibrium of Glauber dynamics in the one phase region II. The general case
    • F. Martinelli and E. Olivieri, Approach to equilibrium of Glauber dynamics in the one phase region II. The general case, Commun. Math. Phys. 161:487-514 (1994).
    • (1994) Commun. Math. Phys. , vol.161 , pp. 487-514
    • Martinelli, F.1    Olivieri, E.2
  • 29
    • 21144477881 scopus 로고
    • Some remarks on pathologies of renormalization group transformations for the Ising model
    • K. Martinelli and E. Olivieri, Some remarks on pathologies of renormalization group transformations for the Ising model, J. Stat. Phys. 72:1169-1177 (1994).
    • (1994) J. Stat. Phys. , vol.72 , pp. 1169-1177
    • Martinelli, K.1    Olivieri, E.2
  • 30
    • 21844483152 scopus 로고
    • Instability of renormalization group pathologies under decimation
    • F. Martinelli and E. Olivieri, Instability of renormalization group pathologies under decimation, J. Stat. Phys. 79:25-42 (1995).
    • (1995) J. Stat. Phys. , vol.79 , pp. 25-42
    • Martinelli, F.1    Olivieri, E.2
  • 31
    • 21844513092 scopus 로고
    • For 2-D lattice spin systems weak mixing implies strong mixing
    • F. Martinelli, C. Olivieri, and R. Schonmann, For 2-D lattice spin systems weak mixing implies strong mixing. Commun. Math. Phys. 165:33-47 (1994).
    • (1994) Commun. Math. Phys. , vol.165 , pp. 33-47
    • Martinelli, F.1    Olivieri, C.2    Schonmann, R.3
  • 32
    • 0001274676 scopus 로고
    • Renormalization theory for Ising-like spin systems
    • C. Domb and M. S. Green, eds. Academic Press, New York
    • Th. Niemeijer and M. J. van Leeuwen, Renormalization theory for Ising-like spin systems, in Phase Transitions and Critical Phenomena, Vol. 6, C. Domb and M. S. Green, eds. (Academic Press, New York, 1976).
    • (1976) Phase Transitions and Critical Phenomena , vol.6
    • Niemeijer, Th.1    Van Leeuwen, M.J.2
  • 33
    • 0009286532 scopus 로고
    • On a cluster expansion for lattice spin systems: A finite size condition for the convergence
    • E. Olivieri, On a cluster expansion for lattice spin systems: A finite Size condition for the convergence, J. Stat. Phys. 50: 1179-1200 (1988).
    • (1988) J. Stat. Phys. , vol.50 , pp. 1179-1200
    • Olivieri, E.1
  • 34
    • 0000049577 scopus 로고
    • Cluster expansion for D-dimensional lattice systems and finite volume factorization properties
    • E. Olivieri and P. Picco, Cluster expansion for D-dimensional lattice systems and finite volume factorization properties, J. Stat. Phys. 59:221-256 (1990).
    • (1990) J. Stat. Phys. , vol.59 , pp. 221-256
    • Olivieri, E.1    Picco, P.2
  • 35
    • 0001944670 scopus 로고
    • Projections of Gibbs measures may be non-Gibbsian
    • R. H. Schonmann, Projections of Gibbs measures may be non-Gibbsian. Commun. Math. Phys. 124:1-7 (1989).
    • (1989) Commun. Math. Phys. , vol.124 , pp. 1-7
    • Schonmann, R.H.1
  • 36
    • 0009268093 scopus 로고
    • Uniqueness and half-space non-uniqueness of Gibbs states in Czech models
    • S. Shlosman, Uniqueness and half-space non-uniqueness of Gibbs states in Czech models, Theor. Math. Phys. 66:284-293 (1986).
    • (1986) Theor. Math. Phys. , vol.66 , pp. 284-293
    • Shlosman, S.1
  • 37
    • 0001964043 scopus 로고
    • Potentials for almost Markovian random fields
    • W. G. Sullivan, Potentials for almost Markovian random fields, Commun. Math. Phys. 33:61-74 (1973).
    • (1973) Commun. Math. Phys. , vol.33 , pp. 61-74
    • Sullivan, W.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.