English

Exponential decay of correlations in the two-dimensional random field Ising model

Probability 2020-11-18 v3

Abstract

We study random field Ising model on Z2\mathbb Z^2 where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.

Keywords

Cite

@article{arxiv.1905.05651,
  title  = {Exponential decay of correlations in the two-dimensional random field Ising model},
  author = {Jian Ding and Jiaming Xia},
  journal= {arXiv preprint arXiv:1905.05651},
  year   = {2020}
}

Comments

1, This document merges arXiv:1902.03302 and a previous version arXiv:1905.05651v2. The title and abstract are revised accordingly. 2, We also improved exposition by incorporating comments from two anonymous referees