Computer simulations of the classical one-dimensional XY-model

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Abstract
Results are presented for the static and time‐dependent behavior of the classical one‐dimensional XY‐model at finite temperatures. Equilibrium properties were determined using an importance sampling Monte Carlo method. A spin‐dynamics computer simulation method was then used to evaluate spin‐spin and energy‐energy time‐displaced correlation functions out to time t=10J−1 using initial states chosen from the equilibrium distribution. The transverse spin‐spin auto correlation function decreases smoothly as a function of time. The longitudinal spin‐spin correlation functions, however, show temperature dependent oscillatory behavior. At moderately high temperature the energy‐energy correlations show diffusive t−1/2 behavior at long times with only a slow temperature dependence of the diffusion constant.