Time-dependent spin correlations in the heisenberg magnet at infinite temperature

A coupled-mode theory of spin fluctuations in the d-dimensional Heisenberg magnet at infinite temperature is used to predict the time dependence of various spin correlation functions. The real-space spin autocorrelation function is shown to have a long-time behaviour approximately (1/t)d theta / where theta =(4+d)/2. Properties at intermediate values of the time are extracted from the theory by numerical analysis. In this time window, the reciprocal-lattice spin autocorrelation function, G(q, t), is, to a good approximation, an exponential function of time. The decay rate is proportional to qalpha , where q is the wavevector. Analysis of our numerical data indicates that the exponent alpha depends weakly on d, and it is significantly different from the value 2 which is compatible with a spin diffusion model. In the asymptotic limit, defined by q to 0, t to infinity , and q2t to 0, G(q,t) is a function of a single variable=(tqtheta ). This result rules against the validity of a diffusion model also in the asymptotic limit.