Monte-Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang-Landau algorithm

TL;DR

This study uses Monte Carlo simulations with the Wang-Landau algorithm to analyze how random site dilution affects the critical properties of the 2D Ising model, revealing insights into universality and critical exponents.

Contribution

It provides a detailed finite-size scaling analysis of the diluted 2D Ising model using Wang-Landau sampling, highlighting the impact of disorder on critical exponents and universality.

Findings

Correlation length exponent ν > 1

Negative α/ν ratio supports weak universality

Critical exponents differ from pure Ising model

Abstract

The influence of random site dilution on the critical properties of the two-dimensional Ising model on a square lattice was explored by Monte Carlo simulations with the Wang-Landau sampling. The lattice linear size was $L = 20-120$ and the concentration of diluted sites $q=0.1, 0.2, 0.3$. Its pure version displays a second-order phase transition with a vanishing specific heat critical exponent $\alpha$, thus, the Harris criterion is inconclusive, in that disorder is a relevant or irrelevant perturbation for the critical behavior of the pure system. The main effort was focused on the specific heat and magnetic susceptibility. We have also looked at the probability distribution of susceptibility, pseudocritical temperatures and specific heat for assessing self-averaging. The study was carried out in appropriate restricted but dominant energy subspaces. By applying the finite-size scaling analysis, the correlation length exponent $\nu$ was found to be greater than one, whereas the ratio of the critical exponents ($\alpha /\nu$) is negative and ($\gamma /\nu$) retains its pure Ising model value supporting weak universality.