Mean-field theory is exact for the random-field model with long-range interactions
Statistical Mechanics
2015-06-18 v2
Abstract
We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To treat random fields, we evoke the self-averaging property of a function of random fields, without recourse to the replica method. The result is that the mean-field theory gives the exact expression of the canonical free energy for systems with power-decaying interactions if the power is smaller than or equal to the spatial dimension.
Cite
@article{arxiv.1402.1581,
title = {Mean-field theory is exact for the random-field model with long-range interactions},
author = {Junichi Tsuda and Hidetoshi Nishimori},
journal= {arXiv preprint arXiv:1402.1581},
year = {2015}
}
Comments
15pages, 1 figure To be published in J. Phys. Soc. Jpn