Random-field Ising model: Insight from zero-temperature simulations

TL;DR

This study uses zero-temperature simulations and advanced algorithms to analyze the critical behavior of the 3D random-field Ising model, revealing shared universality class and clarifying critical exponents.

Contribution

It introduces a computational approach using maximum-flow mapping and push-relabel algorithm to estimate critical parameters and universality class of the 3D RFIM at zero temperature.

Findings

Estimated critical field and exponent for both models.

Confirmed shared universality class of Gaussian and trimodal RFIM.

Resolved controversy over the specific heat critical exponent.

Abstract

We enlighten some critical aspects of the three-dimensional ($d=3$) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian random-field Ising model and an equal-weight trimodal random-field Ising model. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes $\mathcal{V}=L\times L\times L$, where $L$ denotes linear lattice size and $L_{\rm max}=156$. Using as finite-size measures the sample-to-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field $h_{\rm c}$ and the critical exponent $\nu$ of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian random-field Ising model at the best-known value of the critical field provide the magnetic exponent ratio $\beta/\nu$ with high accuracy and clear out the controversial issue of the critical exponent $\alpha$ of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy- and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.