Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model

TL;DR

This paper provides a high-precision numerical estimate of the specific heat exponent in the 4D random-field Ising model, confirming diverging heat capacity behavior and exploring modified hyperscaling relations.

Contribution

The study offers the first high-precision estimate of the specific heat exponent and the critical slowing down exponent in the 4D RFIM using advanced simulation and scaling techniques.

Findings

The specific heat exponent α = 0.12(1), indicating divergence.

Consistency with modified hyperscaling relation.

Estimate of the critical slowing down exponent z.

Abstract

We report a high-precision numerical estimation of the critical exponent $\alpha$ of the specific heat of the random-field Ising model in four dimensions. Our result $\alpha = 0.12(1)$ indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of $\theta$ via the anomalous dimensions $\eta$ and $\bar{\eta}$. Our analysis benefited form a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent $z$ of the maximum-flow algorithm used is also provided.