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.

arXiv comment18 pages, 5 figure

References in corpus (14)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Critical Exponents of the Three Dimensional Random Field Ising Model
• Critical Exponents of the Three Dimensional Random Field Ising Model
• Ising exponents in the two-dimensional site-diluted Ising model
• Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm
• Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
• Estimation of critical behavior from the density of states in Classical Statistical Models
• Critical behaviour of the 2d spin diluted Ising model via the equilibrium ensemble approach
• Entropic sampling via Wang-Landau random walks in dominant energy subspaces
• Specific heat of two-dimensional diluted magnets
• On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
• Crossover and self-averaging in the two-dimensional site-diluted Ising model
• Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems
• The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model

Cited by in corpus (9)

• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• 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
• The Sherrington-Kirkpatrick spin glass model in the presence of a random field with a joint Gaussian probability density function for the exchange interactions and random fields
• Effective field theory for the Ising model with a fluctuating exchange integral in an asymmetric bimodal random magnetic field: A differential operator technique