On an invariance principle for phase separation lines

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 41, Issue 5, 2005, Pages 871-885

  Greenberg, Lev ^a   Ioffe, Dmitry ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Brownian bridge; Ising model; Local limit theorems; Ornstein Zernike decay of correlations; Random path representation; Renormalization; Ruelle operator

Indexed keywords

EID: 23944504039     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2005.05.001     Document Type: Article

References (23)

1. D.B. Abraham P. Reed Interface profile of the Ising ferromagnet in two dimensions Commun. Math. Phys. 49 1 1976 35-46
2. M. Aizenman D.J. Barsky R. Fernández The phase transition in a general class of Ising-type models is sharp J. Statist. Phys. 47 3/4 1987 342-374
3. A. Akutsu N. Akutsu Relationship between the anisotropic interface tension, the scaled interface width and the equilibrium shape in two dimensions J. Phys. A: Math. Gen. 19 1986 2813-2820
4. J. Bricmont J. Fröhlich Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models Commun. Math. Phys. 98 4 1985 553-578
5. J. Bricmont J.L. Lebowitz C.-E. Pfister On the local structure of the phase separation line in the two-dimensional Ising system J. Statist. Phys. 26 2 1981 313-332
6. d Ann. Probab. 30 2002 652-682
7. c Probab. Theory Related Fields 125 3 2003 305-349
8. M. Campanino D. Ioffe Y. Velenik Random path representation and sharp correlations asymptotics at high-temperatures in: Stochastic Analysis on Large Scale Interacting Systems in: Adv. Stud. Pure Math. vol. 39 2004 Math. Soc. Japan Tokyo 29-52
9. R. Dobrushin A statistical behaviour of shapes of boundaries of phases in: R. Kotecký (Ed.) Phase Transitions: Mathematics, Physics, Biology..., 1993 World Scientific Singapore 60-70
10. R. Dobrushin O. Hryniv Fluctuations of shapes of large areas under paths of random walks Probab. Theory Related Fields 105 4 1996 423-458
11. R. Dobrushin O. Hryniv Fluctuations of the phase boundary in the 2D Ising ferromagnet Commun. Math. Phys. 189 2 1997 395-445
12. R. Dobrushin R. Kotecký S. Shlosman Wulff construction. A global shape from local interaction Transl. Math. Monographs vol. 104 1992 American Mathematical Society Providence, RI
13. R. Durrett On the shape of a random string Ann. Probab. 7 1978 1014-1027
14. G. Gallavotti The phase separation line in the two-dimensional Ising model Commun. Math. Phys. 27 1972 103-136
15. Y. Higuchi On some limit theorem related to the phase separation line in the two-dimensional Ising model Z. Wahrsch. Verw. Gebiete 50 3 1979 287-315
16. Y. Higuchi J. Murai J. Wang The Dobrushin-Hryniv theory for the two-dimensional lattice Widom-Rowlinson model Adv. Stud. Pure Math. in press
17. O. Hryniv On local behaviour of the phase separation line in the 2D Ising model Probab. Theory Related Fields 110 1 1998 91-107
18. O. Hryniv R. Kotecký Surface tension and the Ornstein-Zernike behaviour for the 2D Blume-Capel model J. Statist. Phys. 2001
19. D. Ioffe Large deviations for the 2D Ising model: A lower bound without cluster expansions J. Statist. Phys. 74 1-2 1994 411-432
20. Y. Kovchegov The Brownian bridge asymptotics in the subcritical phase of Bernoulli bond percolation model Markov Process. Related Fields 10 2 2004 327-344
21. Ch.-E. Pfister Large deviations and phase separation in the two-dimensional Ising model Helv. Phys. Acta 64 7 1991 953-1054
22. C.-E. Pfister Y. Velenik Large deviations and continuum limit in the 2D Ising model Probab. Theory Related Fields 109 1997 435-506
23. C.-E. Pfister Y. Velenik Interface, surface tension and reentrant pinning transition in the 2D Ising model Commun. Math. Phys. 204 2 1999 269-312