The two-dimensional continuum random field Ising model

TL;DR

This paper constructs a two-dimensional continuum random field Ising model through scaling limits of a perturbed critical Ising model with diminishing disorder, revealing singularity in the magnetisation field law compared to the pure model.

Contribution

It introduces a novel construction of the 2D continuum RFIM via scaling limits and analyzes its law relative to the pure Ising model.

Findings

The continuum RFIM is constructed via scaling limits.

The magnetisation field law is singular with respect to the pure model.

The model is built using white noise perturbations.

Abstract

In this paper we construct the two-dimensional continuum random field Ising model via scaling limits of a random field perturbation of the critical two-dimensional Ising model with diminishing disorder strength. Furthermore, we show that almost surely with respect to the continuum random field given by a white noise, the law of the magnetisation field is singular with respect to that of the two-dimensional continuum pure Ising model constructed by Camia, Garban and Newman.