Aernout C.D. van Enter, Karel Netocny, Hendrikjan G. Schaap
On the Ising model with random boundary condition
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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 give a multi-scale perturbative argument to show that in a sufficiently large volume typical spin configuration under a typical boundary condition contains no interfaces.