Autocorrelation functions of the anisotropic Heisenberg paramagnet in the approximation of a self-consistent fluctuating field

The method proposed earlier for investigating the dynamics of the isotropic Heisenberg paramagnet at high temperatures is generalized to the anisotropic case. A system of nonlinear integrodifferential equations relating the three autocorrelation functions of the $x$, $y$, and $z$ components of an individual spin is obtained. A solution of the system is sought in the form of a series in powers of the time and is investigated on the plane of the complex time variable. The coefficients of the series up to the tenth order for the $xy$ model and the model with truncated dipole interaction are calculated, and the parameters of the singular points nearest the origin are determined from them.