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We study the critical behavior of the Ising model in three dimensions on alattice with site disorder by using Monte Carlo simulations. The disorder iseither uncorrelated or long-range correlated with correlation function thatdecays according to a power-law $r^{-a}$. We derive the critical exponent ofthe correlation length $\nu$ and the confluent correction exponent $\omega$ independence of $a$ by combining different concentrations of defects $0.05 \leqp_d \leq 0.4$ into one global fit ansatz and applying finite-size scalingtechniques. We simulate and study a wide range of different correlationexponents $1.5 \leq a \leq 3.5$ 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 correlateddisorder ensembles and provide estimates for the critical temperatures of thesystem in dependence of the correlation exponent $a$ and the concentrations ofdefects $p_d$. We compare our results to known results from other works and tothe conjecture of Weinrib and Halperin: $\nu = 2/a$ and discuss the occurringdeviations.

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