Critical exponent $ν$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques

Abstract

We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a power-law r −a . We derive the critical exponent of the correlation length ν and the confluent correction exponent ω in dependence of a by combining different concentrations of defects 0.05 ≤ p d ≤ 0.4 into one global fit ansatz and applying finitesize scaling techniques. We simulate and study a wide range of different correlation exponents 1.5 ≤ a ≤ 3.5 as well as the uncorrelated case a = ∞ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent a and the concentrations of defects p d . We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: ν = 2/a and discuss the occurring deviations.