Time-dependent correlations for spin Van der Waals systems

The time-dependent autocorrelation function has been derived for the x component of the total spin for the S=1/2 constant-coupling anisotropic Heisenberg model, i.e., the Van der Waals system. For T>Tc, the time correlation is shown to be Gaussian for both XY-like and Ising-like regimes of the model. For T<Tc, the correlation function is still Gaussian if the model is XY-like; but it is oscillatory if the model is Ising-like. Critical slow down appears only with the Ising-like system for this time-correlation function.