Fluctuations of the phase boundary in the 2d Ising ferromagnet

Communications in Mathematical Physics

Volumn 189, Issue 2, 1997, Pages 395-445

  Dobrushin, R ^c   Hryniv, O ^a,b  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031518868     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050209     Document Type: Article

References (27)

1. DeConinck, J., Dunlop, F., Rivasseau, V.: On the microscopic validity of the Wulff construction and of the generalized Young equation. Commun. Math. Phys. 121, 401-419 (1989)
2. DeConinck, J., Ruiz, J.: Fluctuations of interfaces and anisotropy. J. Phys. A: Math. Gen. 21, L147-153 (1988)
3. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Boston-London: Jones & Bartlett Publishers, 1992
4. Deuschel, J.-D., Stroock, D.W.: Large Deviations. London: Academic Press, 1989
5. Dobrushin, R.: A statistical behaviour of shapes of boundaries of phases. In: Kotecký, R. (ed.) Phase Transitions: Mathematics, Physics, Biology.... Singapore: World Scientific, 1993, pp. 60-70
6. Dobrushin, R., Hryniv, O.: Fluctuations of Shapes of Large Areas under Paths of Random Walks. Probab. Theor. Relat. Fields 105, 423-458 (1996)
7. Dobrushin, R., Kotecký, R., Shlosman, S.: Wulff Construction: A Global Shape from Local Interaction. (Translations of Mathematical Monographs, 104) Providence, R.I.: Amer. Math. Soc., 1992
8. Dobrushin, R., Shlosman, S.: Large and Moderate Deviations in the Ising Model. In: Dobrushin, R. L. (ed.) Probability Contributions to Statistical Mechanics. (Advances in Soviet Mathematics, 20), Providence, R.I.: Amer. Math. Soc. 1994, pp. 91-220
9. Gallavotti, G.: The phase separation line in the two-dimensional Ising model. Commun. Math. Phys. 27, 103-136 (1972)
10. Gikhman, I.I., Skorokhod, A.V.: Introduction to the theory of random processes. Philadelphia: Saunders, 1969
11. Gnedenko, B.V.: The theory of probability. New York: Chelsea, 1962
12. Higuchi, Y.: On some Limit Theorems Related to the Phase Separation Line in the Two-dimensional Ising Model. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 50, 287-315 (1979)
13. Hryniv, O.O. and Dobrushin, R.L.: On Fluctuations of the Wulff Shape in the 2D Ising Model. Uspekhi Mat. Nauk, 50(6), 177-178 (1995)
14. Föllmer, H. and Ort, M.: Large deviations and surface entropy for Markov fields. Asterisque, 157-158, 173-190 (1988)
15. Ioffe, D.: Large Deviations for the 2D Ising Model: A Lower Bound without Cluster Expansions. J. Stat. Phys. 74, 411-432 (1994)
16. c for the Ising model in two dimensions. Probab. Theo. Relat. Fields 102, 313-330 (1995)
17. Kotecký, R., Preiss, D.: Cluster expansions for abstract polymer models. Commun. Math. Phys. 103, 491-498 (1986)
18. Malyshev, V. A., Minlos, R. A.: Gibbs random fields: cluster expansions. Dordrecht: Kluwer, 1991
19. Minlos, R.A. and Sinai, Ya.G.: The phenomenon of "phase separation" at low temperatures in some lattice models of a gas. I. Math. USSR-Sb. 2, 335-395 (1967)
20. Minlos, R.A. and Sinai, Ya.G.: The phenomenon of "phase separation" at low temperatures in some lattice models of a gas. II. Trans. Moscow Math. Soc. 19, 121-196 (1968)
21. Miracle-Sole, S., Ruiz, J.: On the Wulff Construction as a Problem of Equivalence of Statistical Ensembles. In: Fannes, M. et al (eds.) On Three Levels: Micro-, Meso-, and Macro-Approaches in Physics. New York: Plenum Press, 1994, pp. 295-302
22. Mogulskii, A.A.: Large deviations for trajectories of multidimensional random walks. Th. Prob. Appl. 21, 300-315 (1976)
23. Pfister, C.E.: Large deviations and phase separation in the two-dimensional Ising model. Helv. Phys. Acta. 64, 953-1054 (1991)
24. Rockafellar, R.: Convex analysis. Princeton, N.J.: Princeton Univ. Press, 1970
25. Schonmann, R.H.: Second Order Large Deviation Estimates for Ferromagnetic Systems in the Phase Coexistence Region. Commun. Math. Phys. 112, 409-422 (1987)
26. Taylor, J.E.: Unique structure of solutions to a class of nonelliptic variational problems. Proc. Symp. Pure Math. 27, 419-427 (1975)
27. Taylor, J.E.: Some crystalline variational techniques and results. Asterisque 154-155, 307-320 (1987)