On the dynamics of the classical Heisenberg chain

We investigate the space- and time-dependent spin-correlation-function for a linear chain of classical magnetic moments coupled by a purely isotropic exchange interaction. The correlation functions are given in terms of relative variables which at low temperatures turn out to be the normal coordinates appropriate to a system without long-range-order. Analytic expressions for the correlation functions, including correctly the fluctuations responsible for the absence of long-range-order, are given at low temperatures. Well-defined spin wave oscillations exist for wavelengths smaller than the correlation length. In this region our results are consistent with experimental data for the isotropic Heisenberg antiferromagnet TMMC.