Irreversibility in Heisenberg Spin Systems. IV. Time-Dependent Fluctuations at the Curie Point

We propose an approximate solution of the kinetic equations, recently derived by the authors, for the spin autocorrelation function ${\Gamma }_q\mathrm{}\left(t\right)\mathrm{}$ of ferromagnets at the critical point. It is shown that, even for small wave numbers and long times, ${\Gamma }_q\mathrm{}\left(t\right)\mathrm{}$ never reaches a diffusion regime, but decays to zero through damped oscillations. We also compare this theory with previous work on the subject.