Monte Carlo Simulations of Spin-Diffusion in a 2-D Heisenberg Paramagnet

Abstract

We study spin diffusion and spin waves in paramagnetic quantum crystals (solid 3He, for example) by direct simulation of a square lattice of atoms interacting via a nearest-neighbor Heisenberg exchange Hamiltonian. Recently, Cowan and Mullin have used a moments method to study spin transport at arbitrary polarizations. We test their analytic results by calculating the statistical spin correlation function from molecular dynamics simulations using a Monte Carlo algorithm to average over initial spin configurations. Since it is not practical to diagonalize the S\({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}\) exchange Hamiltonian for a lattice which is of sufficient size to study long-wavelength (hydrodynamic) fluctuations, we instead study the S→∞ limit and treat each spin as a vector with a classical equation of motion. We compare our simulations with the assumptions of the moments method regarding the short-time behavior and the long exponential tail of the correlation function. We also present our numerical results for the polarization dependence of the longitudinal spin diffusion coefficient and the complex transverse spin diffusion coefficient.