Phase Diagram of the 3D Bimodal Random-Field Ising Model

TL;DR

This paper introduces an advanced Wang-Landau method with an extrapolation scheme to accurately determine the phase diagram and critical properties of the 3D bimodal random-field Ising model, improving understanding of its phase transition behavior.

Contribution

The paper develops a generalized Wang-Landau approach with an extrapolation scheme for two-parameter density of states, enabling precise analysis of the 3D bimodal RFIM's phase diagram.

Findings

Accurate estimation of the critical disorder strength.

Finite-size scaling approach for phase diagram analysis.

Agreement of critical exponents with previous ground-state studies.

Abstract

The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM). The present approach generalizes our earlier WL implementations, by handling the final stage of the WL process as an entropic sampling scheme, appropriate for the recording of the required two-parametric histograms. We test the accuracy of the proposed extrapolation scheme and then apply it to study the size-shift behavior of the phase diagram of the 3D bimodal RFIM. We present a finite-size converging approach and a well-behaved sequence of estimates for the critical disorder strength. Their asymptotic shift-behavior yields the critical disorder strength and the associated correlation length's exponent, in agreement with previous estimates from ground-state studies of the model.