2004/08/31 by A. C. D. van Enter, A. C. D. van. Enter, Karel Netočný +3 · 1 citation
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Chaotic #Computer science #Gibbs measure #Ising model #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Physics #Sequence (biology) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamic limit #math-ph #math.MP #msc:60F05 #msc:82B20 #msc:82B44
paper · pdf · doi:10.1007/s10955-004-2138-2
published as J. Stat. Phys. 118:997-1056 (2005) · 55 pages, minor corrections and 7 figures added, to appear in J. Stat. Phys
arxiv created 2004/11/08 · openalex publication_date 2005/03/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the `+' and `-' phases are the only almost sure limit Gibbs measures, assuming that the limit is taken along a sparse enough sequence of squares. In particular, we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces. In order to exclude mixtures as possible limit points, a detailed multi-scale contour analysis is performed.