Chaotic size dependence in the Ising model with random boundary conditions
Mathematical Physics
2007-05-23 v2 math.MP
Probability
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.
Cite
@article{arxiv.math-ph/0108011,
title = {Chaotic size dependence in the Ising model with random boundary conditions},
author = {A. C. D. van Enter and I. Medved and K. Netocny},
journal= {arXiv preprint arXiv:math-ph/0108011},
year = {2007}
}
Comments
LaTeX2e, 30 pages, no figures