Critical Exponents of the Three Dimensional Random Field Ising Model

TL;DR

This study uses extensive Monte Carlo simulations to determine critical exponents of the 3D random field Ising model, revealing mixed signs of a first order transition with no latent heat and supporting the droplet picture.

Contribution

It provides the first comprehensive determination of multiple critical exponents for the 3D RFIM using finite size scaling in Monte Carlo simulations.

Findings

Magnetization and disconnected susceptibility exponents suggest a first order transition.

Specific heat saturates, indicating no latent heat.

Sample fluctuations support the droplet model.

Abstract

The phase transition of the three--dimensional random field Ising model with a discrete ($\pm h$) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the exponents for the magnetization and disconnected susceptibility are consistent with a first order transition, the specific heat appears to saturate indicating no latent heat. Sample to sample fluctuations of the susceptibilty are consistent with the droplet picture for the transition.