Space-Time Magnetic Spin Correlations of Anisotropic Heisenberg Systems by the Method of Moments of a Diffusivity - Spectral Representation

The longitudinal and transverse time-dependent spin correlations of Heisenberg spin systems with cylindrical symmetry and with both uniaxial and exchange anisotropy are evaluated in the limit of elevated temperature, by the method of frequency moments. The zeroth, second, and fourth frequency moments are determined by thermal expansions of commutators of equal-time spin operators and their time derivatives. The frequency wave-vector spectral functions are established by these moments via the hydrodynamical representation, based on a two-parameter Gaussian diffusivity. The moment equations in a generic form apply for all spins, for arbitrary range of the exchange interactions, and for arbitrary dimensionality and lattice structures and are particularized with next nearest neighbor interactions for a linear chain, a two-dimensional net and a simple cubic lattice. The effects on the correlation functions of varying the axial anisotropy, the exchange anisotropy, and the interaction range are investigated. The resulting time-dependent correlations and their Fourier transforms are calculated, exhibiting features predicted by theoretical considerations and pointing to several conclusions.