Abstract
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.
Original language | English |
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Pages (from-to) | 997-1056 |
Journal | Journal of Statistical Physics |
Volume | 118 |
Issue number | 5-6 |
DOIs | |
Publication status | Published - 2005 |