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1st Order Phase-transitions in Lattice and Continuous Systems - Extension of Pirogov-sinai Theory

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Bricmont, Jean [UCL] Kuroda, K. Lebowitz, JL.
Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 1985
Language Anglais
Journal information "Communications in Mathematical Physics" - Vol. 101, no. 4, p. 501-538 (1985)
Peer reviewed yes
Publisher Springer Verlag (New York)
issn 0010-3616
e-issn 1432-0916
Publication status Publié
Affiliation UCL - SC/PHYS - Département de physique
Links
  1. Peierls, R.: On Ising's model of ferromagnetism. Proc. Camb. Philos. Soc.32, 477 (1936)
  2. Dobrushin, R.L.: Existence of a phase transition in two- and three-dimensional lattice models. Theory Probab. Appl.10, 193 (1965)
  3. Griffiths, R.B.: Peierls' proof of spontaneous magnetization of a two-dimensional Ising ferromagnet. Phys. Rev. A136, 437 (1964)
  4. Ruelle, D.: Existence of a phase transition in a continuous classical system. Phys. Rev. Lett.27, 1040 (1971)
  5. Sinai, Ya. G.: Theory of phase transitions: Rigorous results. New York: Pergamon Press, 1982.
  6. Original papers:Pirogov, S.A., Sinai, Ya. G.: Phase diagram of classical lattice systems I and II: Theor. Math. Phys.25, 1185 (1976) and26, 39 (1976)
  7. Pirogov, S.A., Sinai, Ya. G.: Ground states in two-dimensional Boson quantum field theory. Ann. Phys.109, 393 (1977)
  8. Imbrie, J.Z.: Phase diagrams and cluster expansions for low temperatureP(?)2 models I and II. Commun. Math. Phys.82, 261 (1981) and82, 305 (1981). For earlier results on phase transitions in quantum field theories, see: Glimm, J., Jaffe, A.: Quantum Physics. A functional integral point of view. New York: Springer 1981 (and references therein)
  9. Slawny, J.: Low temperature expansion for lattice systems with many ground states. J. Stat. Phys.26, 711 (1973). Low temperature properties of classical lattice systems: Phase transitions and phase diagrams. To appear in: ?Phase transitions and critical phenomena,? Vol. 10. Domb, C., Lebowitz, J.L. (eds.), New York: Academic Press 1985
  10. Zahradnik, M.: An alternate version of Pirogov-Sinai theory. Commun. Math. Phys.93, 559 (1984)
  11. Kotecky, R., Preiss, D.: An inductive approach to Pirogov-Sinai theory. Proc. Winter School on Abstract Analysis 1983. Suppl. Ai. Rend Circ. Mat. Palermo (1983)
  12. Malyshev, V.A., Minlos, R.A., Petrova, E.N., Teletski, A.: Generalized contour models (in Russian). Surveys of Science and Technology, pp. 3?54. Theory of probability, mathematical statistics and theoretical cybernetics, Vol. 19. Viniti 1982
  13. Bricmont, J., Kuroda, K., Lebowitz, J.L.: The structure of Gibbs states and phase coexistence for non-symmetric continuum Widom-Rowlinson models. Z. Wahrscheinlichkeitstheor. Verw. Geb.67, 121?138 (1984)
  14. Dobrushin, R.L., Zahradnik, M.: Phase diagrams for the continuous spin models. Extension of Pirogov-Sinai theory. Preprint
  15. Dinaburg, E.I., Sinai, Ya.G.: Preprint (in Russian); see also: ?An analysis of ANNNI model by Peierls' contour method?. Commun. Math. Phys.98, 119 (1985)
  16. Kotecky, R., Preiss, D.: In preparation
  17. Kotecky, R., Shlosman, S.B.: First-order transitions in large entropy lattice models. Commun. Math. Phys.83, 493 (1982)
  18. Iagolnitzer, D., Souillard, B.: On the analyticity in the potential in classical statistical mechanics. Commun. Math. Phys.60, 131 (1978), and references therein
  19. Bricmont, J., Kuroda, K., Lebowitz, J.L.: Surface tension and phase coexistence for general lattice systems. J. Stat. Phys.33, 59 (1983)
  20. Laanait, L., Messager, A., Ruiz, J.: Phase coexistence and surface tensions for the Potts model. Preprint
  21. Bricmont, J., Lebowitz, J.L., Pfister, C.-E.: Low temperature expansion for continuous spin Ising models. Commun. Math. Phys.78, 117 (1980)
  22. Widom, B., Rowlinson, J.S.: New model for the study of liquid-vapour phase transitions. J. Chem. Phys.52, 1270 (1970)
  23. Lebowitz, J.L., Penrose, O.: Rigorous treatment of the van der Waals-Maxwell theory of the liquid-vapour transition. J. Math. Phys.7, 98 (1966)
  24. Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Lecture Notes in Physics, Vol. 159. Berlin, Heidelberg, New York: Springer 1982
Bibliographic reference Bricmont, Jean ; Kuroda, K. ; Lebowitz, JL.. 1st Order Phase-transitions in Lattice and Continuous Systems - Extension of Pirogov-sinai Theory. In: Communications in Mathematical Physics, Vol. 101, no. 4, p. 501-538 (1985)
Permanent URL http://hdl.handle.net/2078.1/54994