On an invariance principle for phase separation lines
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 5, pp. 871-885.
@article{AIHPB_2005__41_5_871_0,
     author = {Greenberg, Lev and Ioffe, Dmitry},
     title = {On an invariance principle for phase separation lines},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {871--885},
     publisher = {Elsevier},
     volume = {41},
     number = {5},
     year = {2005},
     doi = {10.1016/j.anihpb.2005.05.001},
     mrnumber = {2165255},
     zbl = {02211228},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2005.05.001/}
}
TY  - JOUR
AU  - Greenberg, Lev
AU  - Ioffe, Dmitry
TI  - On an invariance principle for phase separation lines
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2005
SP  - 871
EP  - 885
VL  - 41
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2005.05.001/
DO  - 10.1016/j.anihpb.2005.05.001
LA  - en
ID  - AIHPB_2005__41_5_871_0
ER  - 
%0 Journal Article
%A Greenberg, Lev
%A Ioffe, Dmitry
%T On an invariance principle for phase separation lines
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 871-885
%V 41
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2005.05.001/
%R 10.1016/j.anihpb.2005.05.001
%G en
%F AIHPB_2005__41_5_871_0
Greenberg, Lev; Ioffe, Dmitry. On an invariance principle for phase separation lines. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 5, pp. 871-885. doi : 10.1016/j.anihpb.2005.05.001. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.05.001/

[1] D.B. Abraham, P. Reed, Interface profile of the Ising ferromagnet in two dimensions, Commun. Math. Phys. 49 (1) (1976) 35-46. | MR

[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. | MR

[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. | MR

[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. | MR

[6] M. Campanino, D. Ioffe, Ornstein-Zernike theory for the Bernoulli bond percolation on Z d , Ann. Probab. 30 (2002) 652-682. | MR | Zbl

[7] M. Campanino, D. Ioffe, Y. Velenik, Ornstein-Zernike theory for finite range Ising models above T c , Probab. Theory Related Fields 125 (3) (2003) 305-349. | MR | Zbl

[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, Adv. Stud. Pure Math., vol. 39, Math. Soc. Japan, Tokyo, 2004, pp. 29-52. | MR | Zbl

[9] R. Dobrushin, A statistical behaviour of shapes of boundaries of phases, in: Kotecký R. (Ed.), Phase Transitions: Mathematics, Physics, Biology 0ex0ex, World Scientific, Singapore, 1993, pp. 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. | MR | Zbl

[11] R. Dobrushin, O. Hryniv, Fluctuations of the phase boundary in the 2D Ising ferromagnet, Commun. Math. Phys. 189 (2) (1997) 395-445. | MR | Zbl

[12] R. Dobrushin, R. Kotecký, S. Shlosman, Wulff construction. A global shape from local interaction, Transl. Math. Monographs, vol. 104, American Mathematical Society, Providence, RI, 1992. | MR | Zbl

[13] R. Durrett, On the shape of a random string, Ann. Probab. 7 (1978) 1014-1027. | MR | Zbl

[14] G. Gallavotti, The phase separation line in the two-dimensional Ising model, Commun. Math. Phys. 27 (1972) 103-136. | MR

[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. | MR | Zbl

[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. | Zbl

[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. | MR | Zbl

[18] O. Hryniv, R. Kotecký, Surface tension and the Ornstein-Zernike behaviour for the 2D Blume-Capel model, J. Statist. Phys. (2001). | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[21] Ch.-E. Pfister, Large deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta 64 (7) (1991) 953-1054. | MR

[22] C.-E. Pfister, Y. Velenik, Large deviations and continuum limit in the 2D Ising model, Probab. Theory Related Fields 109 (1997) 435-506. | MR | Zbl

[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. | MR | Zbl

Cité par Sources :