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

We study the random field Ising model on 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.

Automated summary

In the random field Ising model on Z(2) with i.i.d. Gaussian variables as the external field, the effect of boundary conditions on magnetization in a finite box exponentially decreases as the distance to the boundary increases.