A theory of spin dynamics in the classical two-dimensional Heisenberg magnet

The wavevector-dependent spin autocorrelation function of a classical Heisenberg model on a square lattice is calculated from the coupled-mode theory of spin dynamics. This theory is consistent with the spherical model for static spin correlations; as the temperature, T, approaches zero the inverse correlation length kappa approximately exp(-const/T). For a ferromagnetic exchange coupling, the decay rate of long wavelength fluctuations, Gamma (q), is proportional to q2T1/2 in the limit (q/ kappa ) to infinity , whereas in the opposite, hydrodynamic limit Gamma (q) varies as q2(T 1n( kappa /q))1/2. At the wavevector for incipient antiferromagnetic ordering, the decay rate is proportional to kappa T1/2, while the corresponding decay rate near the Brillouin zone centre is proportional to (q2T1/2/ kappa ). The coupled-mode equations for ferromagnetically and antiferromagnetically coupled models are solved numerically on a fine grid of wavevectors. The spin autocorrelation function, and its power spectrum are surveyed over a wide range of temperatures and wavevectors.