Chaotic size dependence in the Ising model with random boundary conditions

van Enter, A. C. D.; Medved, I.; Netocny, K.

Chaotic size dependence in the Ising model with random boundary conditions

Authors

van Enter, A. C. D.

Medved, I.

Netocny, K.

Description

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.
LaTeX2e, 30 pages, no figures