  We study spin diffusion and spin waves in paramagnetic quantum crystals
(solid He-3, 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=1/2 exchange Hamiltonian for a lattice
which is of sufficient size to study long-wavelength (hydrodynamic)
fluctuations, we instead study the S -> infinity 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.
