Critical frequency dependence of spin correlation functions

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Abstract
If one is interested in the asymptotic q- kappa - omega dependence of frequency-dependent spin correlation functions it is shown that the intricacies of the corresponding mode-coupling equations are greatly reduced by assuming the validity of certain general properties of the correlation functions. A simplified version of the mode-coupling equations results for the frequency-dependent self-energy. The asymptotic solutions of these equations in the entire critical q- kappa - omega region of three-dimensional anisotropic ferromagnets above Tc are presented. The modifications in the omega -dependence brought about by the anisotropy are especially emphasised. The solutions satisfy the intrinsic assumptions self-consistently. The frequency dependence of the self-energy leads to deviations of the shape functions from a Lorentzian line shape. These anomalies are studied for some special cases. Finally the self-energy of isotropic ferro- and antiferromagnets for general dimensions d>2 are derived in order to compare the author's results with recent renormalisation group calculations valid near d=6 and d=4 respectively. The asymptotic q- kappa - omega dependences turn out to be identical in both procedures.