The 3-d Random Field Ising Model at zero temperature

TL;DR

This study numerically investigates the zero temperature 3D Random Field Ising Model, revealing a discontinuous magnetization transition in the infinite volume limit and examining the effects of different random field distributions.

Contribution

It provides new numerical evidence on the nature of phase transitions and universality in the 3D RFIM at zero temperature, especially regarding the magnetization discontinuity.

Findings

Magnetization is discontinuous in the infinite volume limit.

Energy and its first derivative are continuous across the transition.

Different random field distributions affect the finite-size scaling exponent.

Abstract

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $L$ in three dimensions. For each random field configuration we vary the ferromagnetic coupling strength $J$. We find that in the infinite volume limit the magnetization is discontinuous in $J$. The energy and its first $J$ derivative are continuous. The approch to the thermodynamic limit is slow, behaving like $L^{-p}$ with $p \sim .8$ for the gaussian distribution of the random field. We also study the bimodal distribution $h_{i} = \pm h$, and we find similar results for the magnetization but with a different value of the exponent $p \sim .6 $. This raises the question of the validity of universality for the random field problem.