Non-analyticity and the van der Waals limit

Journal of Statistical Physics

Volumn 114, Issue 3-4, 2004, Pages 665-734

  Friedli, S ^a   Pfister, C E ^a  

^a EPFL   (Switzerland)

Author keywords

Kac potentials; Non analyticity; Pirogov Sinai Theory; Singularity at first order phase transition; Van der Waals limit

Indexed keywords

EID: 3543019152     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:joss.0000012506.98828.dd     Document Type: Article

References (24)

1. J. Bricmont, K. Kuroda, and J. L. Lebowitz, First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory, Commun. Math. Phys. 101:501-538 (1985).
2. J. Bricmont and J. Slawny, Phase transitions in systems with a finite number of dominant ground states, J. Statist. Phys. 54:89-161 (1989).
3. A. Bovier and M. Zahradník, The low-temperature phases of Kac-Ising models, J. Statist. Phys. 87:311-332 (1997).
4. A. Bovier and M. Zahradník, Pirogov-Sinai theory for long range spin systems, Markov Process. Related Fields 8:443-478 (2002).
5. M. Cassandro and E. Presutti, Phase transitions in ising systems with long but finite range interactions, Markov Process. Related Fields 2:241-262 (1996).
6. E. I. Dinaburg and Ya. G. Sinai, Contour models with interactions and applications, Selecta Math. Sovietica 7:291-315 (1988).
7. M. E. Fisher, The theory of condensation and the critical point, Physics 3:255-283 (1967).
8. S. Friedli and C.-E. Pfister, On the singularity of the free energy at first order phase transition, to appear in Commun. Math. Phys. (2003).
9. R. B. Griffiths, General correlation inequalities in ising ferromagnets I & II, J. Math. Phys. 8:478-483 (1967). D. G. Kelly and S. Sherman, General griffiths inequalities on correlations in ising ferromagnets, J. Math. Phys. 9:466-484 (1968).
10. R. B. Griffiths, General correlation inequalities in ising ferromagnets I & II, J. Math. Phys. 8:478-483 (1967). D. G. Kelly and S. Sherman, General griffiths inequalities on correlations in ising ferromagnets, J. Math. Phys. 9:466-484 (1968).
11. S. N. Isakov, Nonanalytic features of the first order phase transition in the ising model, Commun. Math. Phys. 95:427-443 (1984).
12. S. N. Isakov, Phase diagrams and singularity at the point of a phase transition of the first kind in lattice gas models, Teoret. Mat. Fiz. 71:426-440 (1987).
13. K. Kuratowski, Topology, Vols. 1 and 2 (Academic Press, 1968).
14. M. Kac, G. E. Uhlenbeck, and P. C. Hemmer, On the van der Waals theory of the vapor-liquid equilibrium, J. Math. Phys. 4:216-228 (1963).
15. J. S. Langer, Theory of the condensation point, Ann. Physics 41:108-157 (1967).
16. J. L. Lebowitz, A. E. Mazel, and E. Presutti, Liquid-vapor phase transitions for systems with finite range interactions, J. Statist. Phys. 94:955-1025 (1999).
17. J. L. Lebowitz and O. Penrose, Rigorous treatment of the van ver Waals-Maxwell theory of the liquid-vapor transition, J. Math. Phys. 7:98-113 (1966).
18. C. N. Yang and T. D. Lee, Statistical theory of state and phase transition I & II, Phys. Rev. 87:404-419 (1952).
19. C.-E. Pfister, Large deviations and phase separation in the two dimensional ising model, Helv. Phys. Acta 64:953-1054 (1991).
20. E. Presutti, From Statistical Mechanics to Continuum Mechanics, Lecture Notes (Max Planck Institute, Leipzig, 1999).
21. S. A. Pirogov and Ya. G. Sinai, Phase diagrams of classical lattice systems, Teoret. Mat. Fiz. 26:61-76 (1976).
22. Remmert, Theory of Complex Functions (Springer-Verlag, 1991).
23. J. D. van der Waals, De Continuiteit van den Gas en Vloeistoftoestand, Academic Thesis (Leiden, 1873).
24. M. Zahradník, An alternate version of Pirogov-Sinai theory, Commun. Math. Phys. 93:559-581 (1984).