Scale Invariance in disordered systems: the example of the Random Field Ising Model

TL;DR

This paper demonstrates through numerical simulations that the correlation length in the 3D random field Ising model exhibits strong fluctuations and non-self-averaging behavior at criticality, linked to a bound state formation in the field theory.

Contribution

It reveals the non self-averaging nature of the correlation length in the 3D RFIM and suggests this phenomenon is generic in disordered systems across dimensions.

Findings

Correlation function shows strong fluctuations at criticality.

Correlation length is not self-averaging in finite volumes.

Bound state formation explains the non-perturbative effects.

Abstract

We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this non perturbative phenomenon is not particular to the RFIM in 3-d. It is generic for disordered systems in two dimensions and may also happen in other three dimensional disordered systems.