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

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.

18 pages, 5 figure

References in corpus (2)

• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• Entropic sampling via Wang-Landau random walks in dominant energy subspaces

Cited by in corpus (7)

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• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions
• The random field Ising model with an asymmetric and anisotropic trimodal probability distribution
• Corrections to scaling in the dynamic approach to the phase transition with quenched disorder
• Effective field theory for the Ising model with a fluctuating exchange integral in an asymmetric bimodal random magnetic field: A differential operator technique