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

Abstract

We study random field Ising model on ${\mathbb{Z}}^2$ 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.

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