The memory function in the mode-mode coupling theory for the Heisenberg paramagnet

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Abstract
The equation for the relaxation shape function given by the mode-mode theory is studied in the critical region. The emphasis is put on the long-time behaviour of the memory function. A selfconsistent solution of the approximate equation for the generalized wave-vector-dependent diffusion constant is found in the limits q<-5/2 exp(-Dq2t/2) with an inverse fractional power dependence on t. This leads to the conclusion that the equation of motion in the mode-mode theory does not have a characteristic spin diffusion solution with pure exponential decay for asymptotically large times.