Surface order large deviations for Ising, Potts and percolation models

Probability Theory and Related Fields

Volumn 104, Issue 4, 1996, Pages 427-466

  Pisztora, Agoston ^a,b  

^a NEW YORK UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042416901     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01198161     Document Type: Article

References (37)

1. Aizenman, M.: Rigorous studies of critical behavior II. In: Progress in Physics, vol. 10, pp. 453-481. Basel: Birkhäuser 1985
2. Aizenman, M., Bricmont, J., Lebowitz, J.L.: Percolation of the minority spins in high-dimensional Ising models. J. Statist. Phys. 49, 859-865 (1987)
3. 2 Ising and Potts models. J. Statist. Phys. 50, 1-40 (1988)
4. Alexander, K., Chayes, J.T., Chayes, L.: The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation. Comm. Math. Phys. 131, 1-50 (1990)
5. Antal, P., Pisztora, A.: On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. (to appear)
6. Barsky, D.J., Grimmett, R.G., Newman, C.M.: Percolation in half-spaces: equality of critical densities and continuity of the percolation probability. Probab. Theory Relat. Fields 90, 111-148 (1991)
7. Chayes, J.T., Chayes, L., Newman, C.M.: Bernoulli percolation above threshold: an invasion percolation analysis. Ann. Probab. 15, 1272-1287 (1987)
8. Chayes, J.T., Chayes, L., Schonmann, R.H.: Exponential decay of connectivities in the two-dimensional Ising model. J. Statist. Phys. 49, 433-445 (1987)
9. d. C. R. Acad. Sci. Ser. I, 303, 511-513 (1986)
10. Deuschel, J.-D., Pisztora, A.: Surface order large deviations for high-density percolation. Probab. Theory Relat. Fields (in press)
11. Deuschel, J.-D., Stroock, D.W.: Large deviations. New York: Academic Press 1989
12. Dobrushin, R.L., Kotecky, R., Shlosman, S.: Wulff construction: a global shape from local interaction AMS Translations Series (1992)
13. Durrett, R. and Schonmann, R.H.: Large deviations for the contact process and two dimensional percolation. Probab. Theory Relat. Fields 77, 583-603 (1988)
14. Ellis, R.S.: Entropy, Large deviations and statistical mechanics. Berlin: Springer 1986
15. Edwards, R.G., Sokal, A.D.: Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D 38, 2009-2012 (1988)
16. Föllmer, H., Orey, S.: Large deviations for the empirical field of a Gibbs measure. Ann. Probab. 16, 961-977 (1988)
17. Föllmer, H., Ort, M.: Large deviations and surface entropy for Markov fields. Asterisque 157-158, 173-190 (1988)
18. Fortuin, C.M.: On the random cluster model. 11. Physica 58, 393-418 (1972)
19. Fortuin, C.M., Kasteleyn, P.W.: On the random cluster model. I. Physica 57, 536-564 (1972)
20. Gandolfi, A.: Thesis. (1989)
21. Grimmett, G.R.: Percolation. Berlin: Springer 1989
22. Grimmett, G.R.: The stochastic random-cluster process, and the uniqueness of random-cluster measures. Preprint (1994)
23. Grimmett, G.R.: Comparison and disjoint occurrence inequalities for random-cluster models. Preprint (1994)
24. Grimmett, G.R., Marstrand J.M.: The supercritical phase of percolation is well behaved. Proc. R. Soc. Lond. Ser. A 430, 439-457 (1990)
25. Den Hollander, F., Keane, M.: Inequalities of FKG type. Physica 138A, 167-182 (1986)
26. Ioffe, D.: Large deviations for the 2D Ising model: a lower bound without cluster expansions. J. Stat. Phys. 74, 411-432 (1993)
27. c. for the Ising model in two dimensions. Preprint (1994)
28. Kesten, H., Zhang, Y.: The probability of a large finite cluster in supercritical Bernoulli percolation. Ann. Probab. 18, 537-555 (1990)
29. Lebowitz, J.L.: Coexistence of phases in Ising ferromagnets. J. Statist. Phys. 16, 463-476 (1977)
30. Lebowitz, J.L., Schonmann, R.H.: Pseudo-free energies and large deviations for non-Gibbsian FKG measures. Probab. Theory Relat. Fields. 77, 49-64 (1988)
31. Newman, C.M.: Ising models and dependent percolation. In: Topics in Statistical Dependence. IMS Lecture Notes, 16, 395-401 (1991)
32. Newman, C.M.: Disordered Ising systems and random cluster representations in Probability and Phase Transition. Kluwer, pp. 247-260 (1993)
33. Olla, S.: Large deviations for Gibbs random fields. Probab. Theory Relat. Fields 77, 395-409 (1988)
34. Penrose, M.D., Pisztora, A.: Large deviations for discrete and continuous percolation. Adv. Appl. Probab. (to appear)
35. Pfister, C.E.: Large deviations and phase separation in the two-dimensional Ising model. Helv. Phys. Acta 64, 953-1054 (1991)
36. Pisztora, A.: Thesis. (1993)
37. Schonmann, R.H.: Second order large deviation estimates for ferromagnetic systems in the phase coexistence region. Comm. Math. Phys. 112, 409-422 (1987)