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تسجيل مستخدم جديدCritical exponent $ u$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
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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 $ u$ and the confluent correction exponent $omega$ in dependence of $a$ by combining different concentrations of defects $0.05 leq p_d leq 0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5 leq a leq 3.5$ 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 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: $ u = 2/a$ and discuss the occurring deviations.
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