Spin Diffusion in the Heisenberg Paramagnet

Abstract

In this paper, two methods are presented for calculating the spin diffusion coefficient, the long-wavelength low-frequency limit of the spin pair correlation function. These methods are used to evaluate this coefficient in the isotropic Heisenberg paramagnet. In the first method, successively higher correlations are neglected, and eventually an approximate nonlinear integral equation is obtained. In the second, a dispersion relation and sum-rule moment relations are utilized. Expressions are obtained for the diffusion coefficient both at high temperatures and near the Curie temperature. The two evaluations of the diffusion constant at high temperatures agree with each other extremely well, and are in qualitative agreement with two previous determinations.