Single-cluster-update Monte Carlo method for the random anisotropy model

A Wolff-type cluster Monte Carlo algorithm for random magnetic models is presented. The algorithm is demonstrated to reduce significantly the critical slowing down for planar random anisotropy models with weak anisotropy strength. Dynamic exponents z less than or similar to 1.0 of best cluster algorithms are estimated for models with ratio of anisotropy to exchange constant D/J = 1.0 on cubic lattices in three dimensions. For these models, critical exponents are derived from a finite-size scaling analysis.