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

Jian Ding, Jiaming Xia

Published 2019-05-14Version 1

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 at any positive temperature the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.