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

TL;DR

This paper proves that in the 2D random field Ising model at zero temperature, the influence of boundary conditions on magnetization diminishes exponentially with distance, highlighting strong decay of correlations.

Contribution

It establishes exponential decay of correlations in the 2D RFIM at zero temperature, a significant result for understanding phase behavior in disordered systems.

Findings

Boundary effects decay exponentially with distance

Magnetization becomes independent of boundary conditions rapidly

Supports the absence of long-range order at zero temperature

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