Critical droplets in metastable states of probabilistic cellular automata

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 4, 1999, Pages 3935-3941

  Bigelis, Stephen ^a   Cirillo, Emilio N M ^b   Lebowitz, Joel L ^a   Speer, Eugene R ^a  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; COMPUTER SIMULATION; MAGNETIC FIELD EFFECTS; MAGNETIZATION; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; MONTE CARLO METHODS; PROBABILITY;

CELLULAR AUTOMATA; CRITICAL DROPLETS; GLAUBER DYNAMICS; PARALLEL DYNAMICS;

DROP FORMATION;

EID: 0032606957     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.3935     Document Type: Article

References (38)

1. O. Penrose and J. L. Lebowitz, in “Molecular theory of metastability: An update,” appendix to the reprinted edition of the paper by the same authors, “Towards a rigorous molecular theory of metastability,” in Fluctuation Phenomena, 2nd ed., edited by E. W. Montroll and J. L. Lebowitz (North-Holland Physics, Amsterdam, 1987).
2. S. N. Isakov, Commun. Math. Phys. 95, 427 (1984).
3. O. Lanford and D. Ruelle, Commun. Math. Phys. 13, 194 (1969).
4. R. B. Griffiths, C. Y. Weng, and J. S. Langer, Phys. Rev. 149, 301 (1966).
5. M. Cassandro, A. Galves, E. Olivieri, and M. E. Vares, J. Stat. Phys. 35, 603 (1984).
6. E. J. Neves and R. H. Schonmann, Commun. Math. Phys. 137, 209 (1991)
7. E. J. NevesR. H. SchonmannProb. Theor. Rel. Fields 91, 331 (1992)
8. R. H. Schonmann, Commun. Math. Phys. 147, 231 (1992).
9. G. Ben Arous and R. Cerf, Electronic Journal of Probability 1, Paper No. 10 (1996).
10. E. N. M. Cirillo and J. L. Lebowitz, J. Stat. Phys. 90, 211 (1998).
11. E. N. M. Cirillo and E. Olivieri, J. Stat. Phys. 83, 473 (1996)
12. J. Stat. Phys.R. Kotecky and E. Olivieri, 70, 1121 (1993)
13. J. Stat. Phys.R. KoteckyE. Olivieri75, 409 (1994)
14. F. R. Nardi and E. Olivieri, Markov Proc. and Rel. Fields 2, 117 (1996).
15. E. Olivieri and E. Scoppola, J. Stat. Phys. 79, 613 (1995)
16. J. Stat. Phys.E. OlivieriE. Scoppola84, 987 (1996).
17. R. H. Schonmann, Commun. Math. Phys. 161, 1 (1994)
18. R. H. Schonmann, in Probability and Phase Transition, Vol. 420 of NATO Advanced Study Institute Series C: Mathematical and Physical Sciences, edited by G. Grimmett (Kluwer Academic, Dordrecht, 1994), pp. 265–301
19. R. H. Schonmann, S. B. Shlosman, Commun. Math. Phys. 194, 389 (1998).
20. K. Binder, Phys. Rev. B 8, 3423 (1973)
21. Phys. Rev. BK. Binder and H. Müller-Krumbhaar, 9, 2328 (1974)
22. K. Binder and E. Stoll, Phys. Rev. Lett. 31, 47 (1973)
23. H. Tomita and S. Miyashita, Phys. Rev. B 46, 8886 (1992).
24. C. C. A. Günther, P. A. Rikvold, and M. A. Novotny, Phys. Rev. Lett. 71, 3898 (1993)
25. C. C. A. GüntherP. A. RikvoldM. A. NovotnyPhysica A 212, 194 (1994)
26. V. Privman and L. S. Schulman, J. Phys. A 15, L231 (1982)
27. V. PrivmanL. S. SchulmanJ. Stat. Phys. 29, 205 (1982).
28. P. A. Rikvold, H. Tomita, S. Miyashita, and S. W. Sides, Phys. Rev. E 49, 5080 (1994).
29. O. N. Stavskaja, Math. USSR Sbornik 21, 395 (1973);A. L. Toom, N. B. Vasilyev, O. N. Stavskaja, L. G. Mitjushin, G. L. Kurdomov, and S. A. Pirogov (unpublished).
30. P. Rujan, J. Stat. Phys. 49, 139 (1987)
31. J. Stat. Phys.A. Georges and P. Le Doussal, 54, 1011 (1989).
32. J. L. Lebowitz, C. Maes, and E. Speer, J. Stat. Phys. 59, 117 (1990)
33. J. L. Lebowitz, C. Maes, and E. Speer, in Probabilistic Cellular Automata: Some Statistical Mechanics Considerations, Lectures in Complex Systems, SFI Studies in the Sciences of Complexity, Lecture Volume II, edited by E. Jen (Addison Wesley, New York, 1990).
34. P. DaiPra (private communication).
35. S. A. Pirogov and Ya. G. Sinai, Theor. Math. Phys. 25, 1185 (1989)
36. Theor. Math. Phys.S. A. PirogovYa. G. Sinai26, 39 (1989);Ya. G. Sinai, Theory of Phase Transitions: Rigorous Results (Pergamon, Oxford, 1982).
37. P. Ferrari, J. L. Lebowitz, and C. Maes, J. Stat. Phys. 49, 295 (1988).
38. J. L. Lebowitz (unpublished).