Chaotic size dependence in the Ising model with random boundary conditions

Details Chaotic size dependence in the Ising model with random boundary conditions Chaotic size dependence in the Ising model with random boundary conditions

2001-08-20

arxiv.org/abs/math-ph/0108011v2

Physics

Mathematical Physics

LaTeX2e, 30 pages, no figures

Scientific paper

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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