Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model

TL;DR

This study investigates the specific heat behavior in the three-dimensional random-field Ising model, revealing a lack of self-averaging and examining finite-size scaling using advanced computational methods.

Contribution

The paper introduces a unified approach combining Wang-Landau and broad histogram methods to study specific heat scaling in the RFIM.

Findings

Lack of self-averaging of the specific heat is demonstrated.

Finite-size scaling of specific heat maxima is analyzed.

The property of non-self-averaging is linked to the saturation behavior of specific heat.

Abstract

We apply the recently developed critical minimum energy subspace scheme for the investigation of the random-field Ising model. We point out that this method is well suited for the study of this model. The density of states is obtained via the Wang-Landau and broad histogram methods in a unified implementation by employing the N-fold version of the Wang-Landau scheme. The random-fields are obtained from a bimodal distribution ($h_{i}=\pm2$), and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from $L=4$ to $L=32$. Observing the finite-size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat. The lack of self-averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above.