Critical exponentνof the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques

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 ${r}^{\ensuremath{-}a}$. We derive the critical exponent of the correlation length $\ensuremath{\nu}$ and the confluent correction exponent $\ensuremath{\omega}$ in dependence of $a$ by combining different concentrations of defects $0.05\ensuremath{\le}{p}_d\ensuremath{\le}0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5\ensuremath{\le}a\ensuremath{\le}3.5$ as well as the uncorrelated case $a=\ensuremath{\infty}$ 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 concentration of defects ${p}_d$. We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: $\ensuremath{\nu}=2/a$, and discuss the occurring deviations.