Critical exponent $\nu$ 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 $\nu$ and the confluent correction exponent $\omega$ in dependence of $a$ by combining different concentrations of defects $0.05\le p_d\le 0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5\le a\le 3.5$ as well as the uncorrelated case $a=\infty$ 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: $\nu =2/a$ and discuss the occurring deviations.

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• Two-dimensional Ising and Potts model with long-range bond disorder: a renormalization group approach
• Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects