Chaos in the Random Field Ising Model

TL;DR

This paper investigates the sensitivity of the random field Ising model's ground states to small disorder perturbations, revealing mild chaos in low dimensions and marginal rearrangements in three dimensions, with implications for experiments.

Contribution

It provides the first detailed analysis of chaos in the RFIM across different dimensions using exact ground state calculations.

Findings

Mild chaos observed in 1D and 2D RFIM

Marginal rearrangements in 3D RFIM

Implications for finite temperature and experimental studies

Abstract

The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos, meaning that the overlap of the old, unperturbed ground state and the new one is smaller than one, but extensive. In three dimensions the rearrangements are marginal (concentrated in the well defined domain walls). Implications for finite temperature variations and experiments are discussed.