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The influence of random site dilution on the critical properties of thetwo-dimensional Ising model on a square lattice was explored by Monte Carlosimulations 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 pureversion displays a second-order phase transition with a vanishing specific heatcritical exponent $\alpha$, thus, the Harris criterion is inconclusive, in thatdisorder is a relevant or irrelevant perturbation for the critical behavior ofthe pure system. The main effort was focused on the specific heat and magneticsusceptibility. We have also looked at the probability distribution ofsusceptibility, pseudocritical temperatures and specific heat for assessingself-averaging. The study was carried out in appropriate restricted butdominant energy subspaces. By applying the finite-size scaling analysis, thecorrelation length exponent $\nu$ was found to be greater than one, whereas theratio of the critical exponents ($\alpha /\nu$) is negative and ($\gamma /\nu$)retains its pure Ising model value supporting weak universality.

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