Partition function zeros at first-order phase transitions: Pirogov-Sinai theory

Journal of Statistical Physics

Volumn 116, Issue 1-4, 2004, Pages 97-155

  Biskup, M ^a   Borgs, C ^b   Chayes, J T ^b   Kotecky R ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MICROSOFT RESEARCH   (United States)

^c CHARLES UNIVERSITY   (Czech Republic)

Author keywords

contour models; Lee Yang theorem; partition function zeros; Pirogov Sinai theory

Indexed keywords

EID: 4344590030     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOSS.0000037243.48527.e3     Document Type: Article

References (21)

1. M. Biskup, C. Borgs, J. T. Chayes, L. J. Kleinwaks, and R. Kotecký, General theory of Lee-Yang zeros in models with first-order phase transitions, Phys. Rev. Lett. 84:4794-4797 (2000).
2. M. Biskup, C. Borgs, J. T. Chayes, L. J. Kleinwaks, and R. Kotecký, Partition function zeros at first-order phase transitions: A general theory, to appear in Commun. Math. Phys.
3. M. Biskup, C. Borgs, J. T. Chayes, and R. Kotecký, Phase diagrams of Potts models in external fields: I. Real fields, in preparation.
4. M. Biskup, C. Borgs, J. T. Chayes, and R. Kotecký, Phase diagrams of Potts models in external fields: II. One complex field, in preparation.
5. C. Borgs and J. Z. Imbrie, A unified approach to phase diagrams in field theory and statistical mechanics, Commun. Math. Phys. 123:305-328 (1989).
6. C. Borgs and R. Kotecký, A rigorous theory of finite-size scaling at first-order phase transitions, J. Stat. Phys. 61:79-119 (1990).
7. R. L. Dobrushin, Estimates of semiinvariants for the Ising model at low temperatures, in Topics in Statistical and Theoretical Physics, R. L. Dobrushin et al., eds., F. A. Berezin Memorial Volume, Transl. Ser. 2, Vol. 177(32) (Amer. Math. Soc., 1996), pp. 59-81.
8. H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter Studies in Mathematics, Vol. 9 (Walter de Gruyter, Berlin, 1988).
9. R. Kotecký and D. Preiss, An inductive approach to PS theory, Proc. Winter School on Abstract Analysis, Suppl. ai Rend, del Mat. di Palermo (1983).
10. R. Kotecký and D. Preiss, Cluster expansion for abstract polymer models, Commun. Math. Phys. 103:491-498 (1986).
11. T. D. Lee and C. N. Yang, Statistical theory of equations of state and phase transitions: II. Lattice gas and Ising model, Phys. Rev. Lett. 87:410 (1952).
12. E. H. Lieb, private communication.
13. E. H. Lieb and A. D. Sokal, A general Lee-Yang theorem for one-component and multi-component ferromagnets, Commun. Math. Phys. 80:153-179 (1981).
14. S. Miracle-Solé, On the convergence of cluster expansions, Physica A 279:244-249 (2000).
15. J. Navrátil, Contour models and unicity of random fields (in Czech), Diploma Thesis, Charles University, Prague (1982).
16. S. A Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Theor. Math. Phys. 25:358-369 (1975). [In Russian]
17. S. A Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems. Continuation, Theor. Math. Phys. 26:61-76 (1976). [In Russian]
18. D. Ruelle, Thermodynamic Formalism (Addison-Wesley, London, Amsterdam, Don Mills, Sydney, Tokyo, 1978).
19. E. Seiler, Gauge theories as a problem of constructive quantum field theory and statistical mechanics, in Lecture Notes in Physics, Vol. 159 (Springer, Berlin, Heidelberg, New York, 1982).
20. Ya. G. Sinai, Theory of Phase Transitions: Rigorous Results (Pergamon Press, New York, 1982).
21. M. Zahradník, An alternate version of Pirogov-Sinai theory, Commun. Math. Phys. 93:559-581 (1984).