Dynamics of the classical planar spin chain

In this paper we pay attention to the classical one-dimensional planar spin system and, in particular, to the dynamics of such a model. We use the Monte Carlo method to calculate the static correlation functions, needed to determine the relaxation functions completely. We are then able to give the results for the in- and out-of-plane component of the relaxation function. At low temperatures the excitations of the out-of-plane component behave as free particles while the excitations of the in-plane component are very similar to the excitations in the Heisenberg chain.