Space-Time Correlations in Anisotropic Heisenberg Paramagnets at Elevated Temperatures

The structure of the space-time-dependent spin-correlation functions for an anisotropic Heisenberg paramagnet with cylindrical symmetry at elevated temperature is analyzed in terms of a two-parameter Gaussian representation representation of the generalized diffusivity. The parameters are chosen so as to exactly preserve the frequency moments, i.e., 〈ω²ⁿ〉K^αα (α=z, x, or y; $n=0, 1, 2$) of the longitudinal and the transverse spectral functions. These moments are calculated for arbitrary spin S, arbitrary range of the exchange interactions, and arbitrary dimensionality. The results for the correlation functions are worked out for one, two, and three dimensions. In the extreme transverse limit, the results are compared with the exactly soluble XY model for a one-dimensional spin-{} system with only nearest-neighbor (transverse) exchange. The agreement of the results is found to be satisfactory.