Computer simulation of the approach to equilibrium in the classical Heisenberg chain

Abstract

Computer studies of the approach to equilibrium in the classical 3-component Heisenberg chain, starting from a configuration with a large staggered magnetization (i. e., far from equilibrium) are reported. The equal time transverse and reduced longitudinal correlations g⊥(ℓ, t) and g∥(ℓ, t), respectively, were monitored for times long enough to show the approach to equilibrium. Results for g⊥ confirm predictions by Nelson and Fisher of wave-like behavior with a propagation speed equal to twice the zero-temperature spin wave velocity. The equilibration of g∥ was found to be slower and diffusive in nature. The fitted diffusivity appears to be comparable to the value of the spin diffusivity for the corresponding equilibrium problem.