Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

TL;DR

This study uses advanced Monte Carlo simulations to examine the critical behavior and universality classes of the 2d random-bond Ising and 3d Blume-Capel models, confirming theoretical predictions.

Contribution

It demonstrates the effectiveness of the Wang-Landau algorithm combined with a critical energy subspace scheme for analyzing complex spin systems.

Findings

Verification of strong universality in 2d random-bond Ising model

Confirmation of 3d Ising universality in the Blume-Capel model

Accurate critical behavior results from the combined simulation scheme

Abstract

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality's hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected $d=3$ Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.