On the Ising model with random boundary condition

Details On the Ising model with random boundary condition On the Ising model with random boundary condition

2004-08-12

arxiv.org/abs/math-ph/0408024v2

J. Stat. Phys. 118:997-1056 (2005)

Physics

Mathematical Physics

55 pages, minor corrections and 7 figures added, to appear in J. Stat. Phys

Scientific paper

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.

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