01-282 Aernout C.D. van Enter, Igor Medved, Karel Netocny

Chaotic Size Dependence in the Ising Model with Random Boundary Conditions (374K, postscript ) Jul 19, 01

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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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