Disappearance of the de Almeida-Thouless line in six dimensions
Disordered Systems and Neural Networks
2015-05-27 v3 Statistical Mechanics
Abstract
We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.
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Cite
@article{arxiv.1102.1675,
title = {Disappearance of the de Almeida-Thouless line in six dimensions},
author = {M. A. Moore and A. J. Bray},
journal= {arXiv preprint arXiv:1102.1675},
year = {2015}
}
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