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≤pd≤0.4 into one global fit ansatz and applying finite-size 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 concentration of defects pd. 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.