Series expansion for high-temperature dynamics of randomly diluted Heisenberg paramagnets

Abstract

Generalizing the recent work of Collins, high-temperature series expansion for the second and the fourth moments of the frequency-wave-vector-dependent susceptibility are given for a magnetically diluted isotropic Heisenberg paramagnet. Both the site and the bond dilutions are treated. Exchange coupling is limited to nearest neighbors; spin magnitudes are arbitrary and the lattice is cubic with either loose or close packing. Combining with the recently given results for the zeroth moment, a phenomenological analysis, based upon a two-parameter Gaussian construct for the generalized diffusivity, is carried out and the behavior of excitations at small wave vectors is examined. Results for space- and time-dependent correlations, and their frequency-wave-vector Fourier transforms, are presented. In view of the limited length of the series, i.e., four terms for the second and only two terms for the fourth moment, the results are expected to be useful only at temperatures $T$, which are two to three times the transition temperature or higher.