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

A nonlinear integrodifferential equation is derived for the autocorrelation function of the Heisenberg paramagnet at high temperatures in the limit of an infinite-dimensional lattice. The solution of this equation on the plane of the complex time variable is investigated. A majorant and a minorant for the autocorrelation function on the imaginary axis are found, together with the nearest singular points. It is shown that at high frequencies the spectral density decreases exponentially. The damping constant and the pre-exponential factor are determined by the method of moments. The moments to tenth order are calculated.