On local behaviour of the phase separation line in the 2D Ising model

Probability Theory and Related Fields

Volumn 110, Issue 1, 1998, Pages 91-107

  Hryniv, Ostap ^a,b  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031632711     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050146     Document Type: Article

References (10)

1. Abraham, D.B., Reed, P.: Diagonal interface in the two-dimensional Ising ferromagnet. J. Phys. A: Math. Gen. 10, L121-L123 (1977)
2. Akutsu, Y., Akutsu, N.: Relationship between the anisotropic interface tension, the scaled interface width and the equilibrium shape in two dimensions J. Phys. A: Math. Gen. 19, 2813-2820 (1986)
3. Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
4. Bricmont, J., Lebowitz, J.L., Pfister, C.-E.: On the local structure of the phase separation line in the two-dimensional Ising system. J. Stat. Physics. 26, 313-332 (1981)
5. Dobrushin, R : A statistical behaviour of shapes of boundaries of phases. In: Kotecký, R. (ed.) Phase Transitions: Mathematics, Physics, Biology. . . pp. 60-70. Singapore: World Scientific 1993
6. Dobrushin, R., Hryniv, O.: Fluctuations of the Phase Boundary in the 2D Ising Ferromagnet. Preprint ESI 355, 1-56 (1996) (to appear in Commun. Math. Phys.)
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. Gallavotti, G.: The phase separation line in the two-dimensional Ising model. Commun. Math. Phys. 27, 103-136 (1972)
9. 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)
10. Hryniv, O.: On a Conditional Invariance Principle for Random Walks. Preprint ESI 400, 1-11 (1996)