Two-Time Spin-Pair Correlation Function of the Heisenberg Magnet at Infinite Temperature

The two-time spin-pair autocorrelation function $\sigma (\overrightarrow{0},t)$ and the Fourier-space transform $I(\overrightarrow{\mathrm{k}},t)$ of the two-time spin-pair correlation function $\sigma ({\overrightarrow{\mathrm{R}}}_{\mathrm{if}},t)$, are expressed in terms of the "friction function" occurring in the generalized Langevin equation for the spin operator $s_i^{\sim }$ and its Fourier-space transform $S_{\overrightarrow{\mathrm{k}}}^z$, respectively. The friction function is determined in the form of a product of a Gaussian distribution function and a power series as a function of time $t$ for the isotropic Heisenberg magnet and the $\mathrm{XY}$ magnet of spin ½ at infinite temperature. By truncating the power series to the exactly known term, satisfactory results are obtained for $I(\overrightarrow{\mathrm{k}},t)$ of the isotropic Heisenberg magnet of the linear chain and sc lattice. Satisfactory results for $\sigma ({\overrightarrow{\mathrm{R}}}_{\mathrm{if}},t)$ are achieved by taking an inverse Fourier-space transform of the thus determined $I(\overrightarrow{\mathrm{k}},t)$.