On the Ising model with random boundary condition

A. C. D. van Enter; K. Netocny; H. G. Schaap

doi:10.1007/s10955-004-2138-2

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On the Ising model with random boundary condition

A. C. D. van Enter·K. Netocny·H. G. Schaap

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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 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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BibTeX RIS

A. C. D. van Enter, K. Netocny, H. G. Schaap. 2004-11-08. On the Ising model with random boundary condition. https://doi.org/10.1007/s10955-004-2138-2

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