Random-cluster analysis of a class of binary lattice gases

Journal of Statistical Physics

Volumn 91, Issue 1-2, 1998, Pages 47-74

  Häggström, Olle ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Gibbs measure; Lattice gas; Phase transition; Random cluster representation; Widom Rowlinson model

Indexed keywords

EID: 0039657245     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023031819217     Document Type: Article

References (26)

1. 2 Ising and Potts models, J. Statist. Phys. 50:1-40 (1988).
2. K. S. Alexander, The asymmetric random cluster process and comparison of Ising and Potts models, preprint (1997).
3. A. J. Baddeley and M. N. M. Van Lieshout, Area-interaction point processes, Ann. Inst. Statist. Math. 46:601-619 (1995).
4. J. Van den Berg and C. Maes, Disagreement percolation in the study of Markov fields, Ann. Probab. 22:749-763 (1994).
5. G. R. Brightwell, O. Häggström, and P. Winkler, Nonmonotonic behavior in hard-core and Widom-Rowlinson models, preprint (1997).
6. R. Burton, and J. Steif. Nonuniqueness of measures of maximal entropy for subshifts of finite type, Ergod. Th. Dynam. Sys. 14:213-236 (1994).
7. R. Burton and J. Steif, New results on measures of maximal entropy, Israel J. Math. 89:275-300 (1995).
8. J. T. Chayes, L. Chayes, and R. Kotecký, The analysis of the Widom-Rowlinson model by stochastic geometric methods. Commun. Math. Phys. 172:551-569 (1995).
9. L. Chayes and J. Machta, Graphical representations and cluster algorithms I. Discrete spin systems, Physica A 239:542-601 (1997).
10. L. Chayes and J. Machta, Graphical representations and cluster algorithms, part II, Physica A, to appear (1997).
11. R. L. Dobrushin, The problem, of uniqueness of a Gibbsian random field and the problem of phase transition. Funct. Anal. Appl. 2:302 312 (1968).
12. C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models, Physica 57:536-564 (1972).
13. C. M. Fortuin, P. W. Kasteleyn, and J. Ginibre. Correlation inequalities on some partially ordered sets, Commun. Math. Phys. 22:89-103 (1971).
14. H.-O. Georgii. Gibbs Measures and Phase Transitions (de Gruyter, New York, 1988).
15. H. -O. Georgii and O. Häggström, Phase transition in continuum Potts models, Commun. Math. Phys. 181:507-528 (1996).
16. G. Giacomin, J. L. Lebowitz, and C. Maes. Agreement percolation and phase coexistence in some Gibbs systems. J. Statist. Phys. 80:1379-1403 (1995).
17. G. Grimmett, Percolation (Springer, New York, 1989).
18. G. Grimmett, The stochastic random-cluster process, and the uniqueness of random-cluster measures, Ann. Probab. 23:1461-1510 (1995).
19. O. Häggström, On phase transitions for subshifts of finite type, Israel J. Math. 94:319-352 (1996).
20. O. Häggström, Random-cluster representations in the study of phase transitions, preprint (1997).
21. R. Holley, Remarks on the FKG inequalities, Commun. Math. Phys. 36:227-231 (1974).
22. J. L. Lebowitz and G. Gallavotti, Phase transitions in binary lattice gases, J. Math. Phys. 12:1129-1133 (1971).
23. T. Lindvall, Lectures on the Coupling Method (Wiley, New York. 1992).
24. D. Ruelle, Existence of a phase transition in a continuous classical system, Phys. Rev. Lett. 27:1040-1041 (1971).
25. V. Strassen, The existence of probability measures with given marginals, Ann. Math. Statist. 36:423-439 (1965).
26. B. Widom and J. S. Rowlinson, New model for the study of liquid-vapor phase transition. J. Chem. Phys. 52:1670-1684 (1970).