On an invariance principle for phase separation lines

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1. [1] D.B. Abraham, P. Reed, Interface profile of the Ising ferromagnet in two dimensions, Commun. Math. Phys.49 (1) (1976) 35-46. MR421542
2. [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. MR894398
3. [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. [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. Zbl1223.82010MR789871
5. [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. MR643712
6. [6] M. Campanino, D. Ioffe, Ornstein–Zernike theory for the Bernoulli bond percolation on $Z^d$, Ann. Probab.30 (2002) 652-682. Zbl1013.60077MR1905854
7. [7] M. Campanino, D. Ioffe, Y. Velenik, Ornstein–Zernike theory for finite range Ising models above $T_c$, Probab. Theory Related Fields125 (3) (2003) 305-349. Zbl1032.60093MR1964456
8. [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. Zbl1074.82015MR2073329
9. [9] R. Dobrushin, A statistical behaviour of shapes of boundaries of phases, in: Kotecký R. (Ed.), Phase Transitions: Mathematics, Physics, Biology $\cdots \phantom{0ex0ex}$, World Scientific, Singapore, 1993, pp. 60-70. 
10. [10] R. Dobrushin, O. Hryniv, Fluctuations of shapes of large areas under paths of random walks, Probab. Theory Related Fields105 (4) (1996) 423-458. Zbl0853.60057MR1402652
11. [11] R. Dobrushin, O. Hryniv, Fluctuations of the phase boundary in the 2D Ising ferromagnet, Commun. Math. Phys.189 (2) (1997) 395-445. Zbl0888.60083MR1480026
12. [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. Zbl0917.60103MR1181197
13. [13] R. Durrett, On the shape of a random string, Ann. Probab.7 (1978) 1014-1027. Zbl0421.60016MR548895
14. [14] G. Gallavotti, The phase separation line in the two-dimensional Ising model, Commun. Math. Phys.27 (1972) 103-136. MR342116
15. [15] Y. Higuchi, On some limit theorem related to the phase separation line in the two-dimensional Ising model, Z. Wahrsch. Verw. Gebiete50 (3) (1979) 287-315. Zbl0406.60084MR554548
16. [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. Zbl1140.82321
17. [17] O. Hryniv, On local behaviour of the phase separation line in the 2D Ising model, Probab. Theory Related Fields110 (1) (1998) 91-107. Zbl0897.60038MR1602044
18. [18] O. Hryniv, R. Kotecký, Surface tension and the Ornstein–Zernike behaviour for the 2D Blume–Capel model, J. Statist. Phys. (2001). Zbl1003.82005MR1882748
19. [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. Zbl0946.82502MR1257822
20. [20] Y. Kovchegov, The Brownian bridge asymptotics in the subcritical phase of Bernoulli bond percolation model, Markov Process. Related Fields10 (2) (2004) 327-344. Zbl1162.82306MR2082577
21. [21] Ch.-E. Pfister, Large deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta64 (7) (1991) 953-1054. MR1149430
22. [22] C.-E. Pfister, Y. Velenik, Large deviations and continuum limit in the 2D Ising model, Probab. Theory Related Fields109 (1997) 435-506. Zbl0904.60022MR1483597
23. [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. Zbl0937.82016MR1704276