# Exponential decay of correlations in the 2D random field Ising model

## TL;DR

This paper extends the analysis of correlation decay in the 2D random field Ising model to positive temperatures with weak disorder, using a novel continuous function representation and disagreement percolation.

## Contribution

It introduces an exact continuous function representation of the order parameter, enabling new decay of correlation results at positive temperatures for weak disorder.

## Key findings

- Proves exponential decay of correlations in the 2D RFIM at positive temperatures
- Extends previous zero-temperature results to positive temperatures
- Uses disagreement percolation for analysis

## Abstract

An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement percolation. This facilitates an extension of the recent analyses of the decay of correlations to positive temperatures, at homogeneous but arbitrarily weak disorder.