On the decay of correlations in the random field Ising model
Mathematical Physics
2018-03-14 v3 math.MP
Probability
Abstract
In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodic-theoretic in nature and does not provide any quantitative information. This article proves the first quantitative version of the Aizenman-Wehr theorem. The proof introduces a new method for proving decay of correlations that may be interesting in its own right. A fairly detailed sketch of the main ideas behind the proof is also included.
Keywords
Cite
@article{arxiv.1709.04151,
title = {On the decay of correlations in the random field Ising model},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:1709.04151},
year = {2018}
}
Comments
16 pages. Proof reorganized for better readability. To appear in Comm. Math. Phys