On the universality class of the 3d Ising model with long-range-correlated disorder

TL;DR

This study investigates the universality class of the 3D Ising model with long-range-correlated disorder using extensive Monte Carlo simulations, revealing critical exponents that depend on the disorder correlations.

Contribution

It provides new numerical estimates of critical exponents for the 3D Ising model with correlated disorder, clarifying discrepancies in previous studies.

Findings

Critical exponents differ from earlier numerical results.

Exponents show dependence on long-range correlation decay.

Supports the extended Harris criterion for correlated disorder.

Abstract

We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion (A. Weinrib, B. I. Halperin, Phys. Rev. B 27 (1983) 413) and bring about the new universality class, the numerical values of the critical exponents found so far differ essentially. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising magnet with non-magnetic impurities arranged as lines with random orientation. We apply Wolff cluster algorithm accompanied by a histogram reweighting technique and make use of the finite-size scaling to extract the values of critical exponents governing the magnetic phase transition. Our estimates for the exponents differ from the results of the two numerical simulations performed so far and are in favour of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlations decay.