Rigorous Analysis of Singularities and Absence of Analytic Continuation at First-Order Phase-Transition Points in Lattice-Spin Models

Physical Review Letters

Volumn 92, Issue 1, 2004, Pages 157021-157024

  Friedli, Sacha ^a   Pfister, Charles Édouard ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSATION; GROUND STATE; HAMILTONIANS; ISOTHERMS; MAGNETIZATION; MAXWELL EQUATIONS; PRESSURE EFFECTS; PROBABILITY; THERMODYNAMICS; VAN DER WAALS FORCES;

NONANALYTIC PROPERTIES; THERMODYNAMIC POTENTIAL;

PHASE TRANSITIONS;

EID: 1242284699     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. J. D. van der Waals, academic thesis, Leiden, 1873.
2. J. E. Mayer, J. Chem. Phys. 5, 67 (1937).
3. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952).
4. H. N. V. Temperley, Proc. Phys. Soc. London Sect. A 67, 233 (1954); S. Katsura, Prog. Theor. Phys. 13, 571 (1955).
5. H. N. V. Temperley, Proc. Phys. Soc. London Sect. A 67, 233 (1954); S. Katsura, Prog. Theor. Phys. 13, 571 (1955).
6. S. Katsura, Adv. Phys. 12, 391 (1963).
7. A. F. Andreev, Sov. Phys. JETP 18, 1415 (1964).
8. M. E. Fisher, Physics (Long Island City, N.Y.) 3, 255 (1967).
9. J. S. Langer, Ann. Phys. (N.Y.) 41, 108 (1967).
10. H. Kunz and B. Souillard, J. Stat. Phys. 19, 77 (1978).
11. C. Newman and L. S. Schulman, J. Math. Phys. (N.Y) 18, 23 (1977).
12. I. G. Enting and R. J. Baxter, J. Phys. A 13, 3723 (1980).
13. V. Privman and L. S. Schulman, J. Stat. Phys. 29, 205 (1982).
14. C.C.A. Günter, P.A. Rikvold, and M. A. Novotny, Phys. Rev. Lett. 71, 3898 (1993).
15. O. Penrose, J. Stat. Phys. 78, 267 (1995).
16. J. L. Meunier and A. Morel, Eur. Phys. J. B 13, 341 (2000).
17. S. N. Isakov, Commun. Math. Phys. 95, 427 (1984).
18. S. N. Isakov, Teor. Mat. Fiz. 71, 426 (1987).
19. O. Lanford and D. Ruelle, Commun. Math. Phys. 13, 194 (1969).
20. R. H. Schonmann and S. Shlosman, Commun. Math. Phys. 194, 389 (1998).
21. 0(ω) ≥ ρ|I(ω)|. That is, regions of incorrect points are energy barriers.
22. S. A. Pirogov and Y. G. Sinai, Teor. Mat. Fiz. 25, 358 (1975); 26, 61 (1976); M. Zahradmk, Commun. Math. Phys. 93, 559 (1984).
23. S. A. Pirogov and Y. G. Sinai, Teor. Mat. Fiz. 25, 358 (1975); 26, 61 (1976); M. Zahradmk, Commun. Math. Phys. 93, 559 (1984).
24. S. A. Pirogov and Y. G. Sinai, Teor. Mat. Fiz. 25, 358 (1975); 26, 61 (1976); M. Zahradmk, Commun. Math. Phys. 93, 559 (1984).
25. S. Friedli and C.-E. Pfister, cond-mat/0212015.
26. J. L. Lebowitz and O. Penrose, J. Math. Phys. (N.Y.) 7, 98 (1966).
27. S. Friedli and C.-E. Pfister, cond-mat/0302480.
28. A. Bovier and M. Zahradník, Markov Process. Related Fields 8, 443 (2002).
29. For Theorem 1 contours are connected components of incorrect points (see [20]). For Theorems 2 and 3 we use a more elaborate notion of contours based on the coarse-graining technique of Bovier and Zahradnik [25].
30. See the discussion in [14], p. 274, before Theorem 1.