Finite-size effects for the Potts model with weak boundary conditions

Journal of Statistical Physics

Volumn 109, Issue 1-2, 2002, Pages 67-131

  Borgs, C ^a   Kotecky R ^b   Medved, I ^c  

^a MICROSOFT RESEARCH   (United States)

^b CHARLES UNIVERSITY   (Czech Republic)

^c NUCLEAR PHYSICS INSTITUTE   (Czech Republic)

Author keywords

Finite size scaling; Lattice systems; Potts model; Surface coupling

Indexed keywords

EID: 0141785333     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019931410450     Document Type: Article

References (27)

1. Y. Imry, Finite-size rounding of a first-order phase transition, Phys. Rev. B 21:2042-2043 (1980).
2. M. E. Fisher and A. N. Berker, Scaling for firt-order phase transitions in thermodynamic and finite systems, Phys. Rev. B 26:2507-2513 (1982).
3. H. W. J. Blöte and M. P. Nightingale, Critical behaviour of the two dimensional Potts model with a continuous number of states; a finite-size scaling analysis, Physica A 112:405-465 (1981).
4. K. Binder, Finite-size scaling analysis of Ising model block distribution functions, Z. Phys. B 43:119-140 (1981).
5. K. Binder and D. P. Landau, Finite-size scaling at first-order phase transitions, Phys. Rev. B 30:1477-1485 (1984).
6. C. Borgs and R. Kotecký, A rigorous theory of finite-size scaling at first-order phase transitions, J. Statist. Phys. 61:79-119 (1990).
7. C. Borgs and R. Kotecký, Finite-size effects at asymmetric first-order phase transitions, Phys. Rev. Lett. 68:1734-1737 (1992).
8. C. Borgs, R. Kotecký, and S. Miracle-Solé, Finite-size scaling for the Potts models, J. Statist. Phys. 62:529-552 (1991).
9. C. Borgs and J. Z. Imbrie, Finite-size scaling and surface tension from effective one dimensional systems, Commun. Math. Phys. 145:235-280 (1992).
10. C. Borgs and J. Z. Imbrie, Crossover finite-size scaling at first-order transitions, J. Statist. Phys. 69:487-537 (1992).
11. C. Borgs, Finite-size scaling for Potts models in long cylinders, Nuclear Phys. B 384: 605-645 (1992).
12. R. Kotecký, and I. Medved', Finite-size scaling for the 2D Ising model with fixed boundary conditions, J. Statist. Phys. 104:905-943 (2001).
13. C. Borgs and R. Kotecký, Surface-induced finite-size effects for the first-order phase transitions, J. Statist. Phys. 79:43-116 (1995).
14. I. Medved', Finite-Size Effects for the Potts Model, Master's thesis (Charles University, Prague, 1996).
15. R. Pemantle and J. Steif, Robust phase transitions for Heisenberg and other models on general trees, Ann. Probab. 27:876-912 (1999).
16. A. van Enter, A remark on the notion of robust phase transitions, J. Statist. Phys. 98:1409-1416 (2000).
17. R. Kotecký and S. B. Shlosman, First-order transitions in large entropy lattice models, Comm. Math. Phys. 83:493-515 (1982).
18. R. B. Griffiths, Correlations in Ising ferromagnets I, II, J. Math. Phys. 8:478-489 (1967); D. G. Kelley and S. Sherman, General Griffiths inequalities on correlations in Ising ferromagnets, J. Math. Phys. 9:466 (1969).
19. R. B. Griffiths, Correlations in Ising ferromagnets I, II, J. Math. Phys. 8:478-489 (1967); D. G. Kelley and S. Sherman, General Griffiths inequalities on correlations in Ising ferromagnets, J. Math. Phys. 9:466 (1969).
20. M. Biskup, C. Borgs, J. T. Chayes, and R. Kotecký, Gibbs states of graphical representations of the Potts model with external fields, J. Math. Phys. 41:1170-1210 (2000).
21. C. M. Fortuin and P. W. Kasteleyn, On the random cluster model I: Introduction and relation to other models, Physica 57:536-564 (1972).
22. D. C. Brydges, A Short Course on Cluster Expansions, Phé nomènes critiques, systèmes aléatoires, théories de jauge, Part I, II (Les Houches, 1984) (North-Holland, Amsterdam, 1986), pp. 129-183.
23. R. L. Dobrushin, Estimates of semi-invariants for the Ising model at low temperatures, in Topics in Statistical and Theoretical Physics (Amer. Math. Soc., Providence, RI, 1996), pp. 59-81.
24. S. Miracle-Solé, On the convergence of cluster expansions. Phys. A 279:244-249 (2000).
25. P. Holický, R. Kotecký, and M. Zahradník, Phase diagram of horizontally invariant Gibbs states for lattice models, Ann. H. Poincaré (2002), in print.
26. R. Kotecký and S. B. Shlosman, Existence of first-order transitions for Potts models, Proc. of the International Workshop - Stochastic Processes in Quantum Theory and Statistical Physics, Vol. 83, pp. 493-515 (1982), S. Albeverio, Ph. Combe, and M. Sirigue-Collins (eds.), Lecture Notes in Physics, Vol. 173 (Springer-Verlag, Berlin/Heidelberg/New York, 1982), pp. 248-253.
27. R. Kotecký and S. B. Shlosman, Existence of first-order transitions for Potts models, Proc. of the International Workshop - Stochastic Processes in Quantum Theory and Statistical Physics, Vol. 83, pp. 493-515 (1982), S. Albeverio, Ph. Combe, and M. Sirigue-Collins (eds.), Lecture Notes in Physics, Vol. 173 (Springer-Verlag, Berlin/Heidelberg/New York, 1982), pp. 248-253.