Critical Exponents of the Three Dimensional Random Field Ising Model

TL;DR

This paper investigates the critical behavior of the 3D random field Ising model using Monte Carlo simulations, finding evidence for a first-order transition with specific heat saturation and droplet-like fluctuations.

Contribution

It provides the first comprehensive determination of multiple critical exponents for this model through finite size scaling analysis.

Findings

Magnetization and disconnected susceptibility exponents suggest a first-order transition.

Specific heat saturates, indicating no latent heat.

Sample fluctuations align with the droplet picture.

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.