Dobrushin–Kotecký–Shlosman Theorem up to the Critical Temperature

Abstract:We develop a non-perturbative version of the Dobrushin–Kotecký–Shlosman theory of phase separation in the canonical 2D Ising ensemble. The results are valid for all temperatures below critical.

[1]  Roberto H. Schonmann,et al.  Complete analyticity for 2D Ising completed , 1995 .

[2]  Y. Akutsu,et al.  Relationship between the anisotropic interface tension, the scaled interface width and the equilibrium shape in two dimensions , 1986 .

[3]  K. Alexander,et al.  Approximation of subadditive functions and convergence rates in limiting-shape results , 1997 .

[4]  S. Shlosman,et al.  Constrained variational problem with applications to the Ising model , 1996 .

[5]  Ãgoston Pisztora,et al.  Surface order large deviations for Ising, Potts and percolation models , 1996 .

[6]  R. Schneider Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[7]  A. Martin-Löf Mixing properties, differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature , 1973 .

[8]  R. Dobrushin,et al.  Large and Moderate Deviations in the Ising Model , 1994 .

[9]  Lower Bounds on the Connectivity Function in all Directions for Bernoulli Percolation in Two and Three Dimensions , 1990 .

[10]  Roberto H. Schonmann,et al.  Wulff Droplets and the Metastable Relaxation of Kinetic Ising Models , 1998 .

[11]  C. Pfister,et al.  Large deviations and continuum limit in the 2D Ising model , 1997 .

[12]  D. Ioffe Large deviations for the 2D ising model: A lower bound without cluster expansions , 1994 .

[13]  R. Dobrushin,et al.  Institute for Mathematical Physics Fluctuations of the Phase Boundary in the 2d Ising Ferromagnet Fluctuations of the Phase Boundary in the 2d Ising Ferromagnet , 2022 .

[14]  J. Chayes,et al.  Exponential decay of connectivities in the two-dimensional ising model , 1987 .

[15]  H. Kesten Asymptotics in High Dimensions For the Fortuin-Kasteleyn Random Cluster Model , 1991 .

[16]  Jennifer Chayes,et al.  The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation , 1990 .

[17]  R. Dobrushin,et al.  The central limit theorem and the problem of equivalence of ensembles , 1977 .

[18]  R. L. Dobrushin,et al.  Wulff Construction: A Global Shape from Local Interaction , 1992 .

[19]  Ornstein-Zernike Behaviour And Analyticity Of Shapes For Self-Avoiding Walks On Z^d , 1998 .

[20]  A. Sokal,et al.  Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. , 1988, Physical review. D, Particles and fields.

[21]  K. Ball CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY , 1994 .

[22]  J. Chayes,et al.  Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models , 1988 .

[23]  F. Martinelli,et al.  On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point , 1996 .

[24]  C. Pfister Large deviations and phase separation in the two-dimensional Ising model , 1991 .