Two-dimensional random field Ising model at zero temperature

I will discuss 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. I will present a recent result that at zero temperature the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary. This is based on joint work with Jiaming Xia.