Central limit theorem for the free energy of the random field Ising model

TL;DR

This paper proves a central limit theorem for the free energy of the random field Ising model across all temperatures and dimensions, resolving a long-standing open problem using Stein's method.

Contribution

It establishes a CLT for the free energy of the RFIM with uniform boundary conditions, covering all temperature regimes and dimensions, solving a problem from 1990.

Findings

CLT holds for free energy of RFIM at all temperatures and dimensions

Uses Stein's method to prove the theorem

Resolves a problem posed by Wehr and Aizenman in 1990

Abstract

A central limit theorem is proved for the free energy of the random field Ising model with all plus or all minus boundary condition, at any temperature (including zero temperature) and any dimension. This solves a problem posed by Wehr and Aizenman in 1990. The proof uses a variant of Stein's method.