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Chaotic size dependence in the Ising model with random boundary conditions

A. C. D. van Enter·I. Medved·K. Netocny
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Abstract

We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.

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A. C. D. van Enter, I. Medved, K. Netocny. 2002-02-28. Chaotic size dependence in the Ising model with random boundary conditions. https://arxiv.org/abs/math-ph/0108011

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