Monte Carlo studies of random anisotropy magnets

Abstract We have carried out systematic studies of the d =2, n =2, HPZ model of random magnetic anisotropy, using standard Monte Carlo methods. The non-random, D =0, case is the usual two-dimensional XY model and exhibits no magnetism or hysteresis at any temperature. We find that at finite D / J (where J is the magnetic exchange) there are significant hysteretic and other irreversible effects. We find, over the Monte Carlo time scales that we run our simulations, four well-delineated regions as a function of temperature: a locked spin glass phase at low T , an intermediate regime in which the spins are correlated to the original directions, a region of algebraic order of the Kosterlitz-Thouless type in which the anisotropy is irrelevant, and a high temperature disordered phase.