DYNAMIC CRITICAL-BEHAVIOR OF THE 3-DIMENSIONAL HEISENBERG-MODEL

We have carried out extensive Monte Carlo simulations of the dynamic critical behavior of L X L X L simple-cubic classical Heisenberg models with periodic boundary conditions. The equilibrium relaxation time tau is determined from the long-time exponential decay of the time-displaced correlation function of the magnetization. Using finite-size scaling and corrections to scaling we find that at the critical point T(c) = (0. 6929)-1, tau grows like tau congruent-to L(z) with z = 1.96(6). In the paramagnetic region we show that the relaxation time is represented by a universal scaling function tauL(-z) vs (T/T(c)-1)L1/nu with z = 1. 96(6). This estimate is consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving dipolar interactions. We also describe how a simple over-relaxation algorithm of Creutz and of Brown and Woch can be incorporated into the Metropolis sampling method for the classical Heisenberg model, thereby significantly reducing the critical slowing down; the resultant correlation time varies as tau approximately(T/T(c)-1)-0.77, which implies z congruent-to 1.10.