Universality in Random Systems: the case of the 3-d Random Field Ising model

TL;DR

This study numerically investigates the 3D Random Field Ising Model at zero temperature across various lattice sizes and disorder distributions, revealing non-universal critical exponents and challenging the universality hypothesis in disordered systems.

Contribution

It provides the first comprehensive numerical analysis of the 3D RFIM with multiple disorder types, demonstrating the breakdown of universality in critical behavior.

Findings

Different critical exponents for various disorder distributions

Magnetization discontinuity at infinite volume limit

Disagreement with universality hypothesis

Abstract

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $ 6 \le L \le 90 $ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each random field configuration we vary the ferromagnetic coupling strength J and compute the ground state exactly. We examine the case of different random field probability distributions: gaussian distribution, zero width bimodal distribution h_{i} = \pm 1, wide bimodal distribution h_{i} = \pm 1 +\delta h (with a gaussian $\delta h$). We also study the case of the randomly diluted antiferromagnet in a field,which is thought to be in the same universality class. We find that in the infinite volume limit the magnetization is discontinuous in J and we compute the relevant exponent, which, according to finite size scaling, equals $ 1/ \nu $ . We find different values of $ \nu $ for the different random field distributions, in disagreement with universality.