Singular Behavior of the Spectral-Weight Function of the Spin-Pair Correlation Function

It is pointed out that, when the spin diffusion occurs, the spectral weight function $\tilde{\sigma }({\overrightarrow{\mathrm{R}}}_{\mathrm{if}},\omega )$ of the two-time spin-pair correlation function becomes singular at $\omega =0\mathrm{}$. The singular behavior is given for the one-, two-, and three-dimensional Heisenberg magnet at infinite temperature. The result is illustrated by the theoretical curves of $\tilde{\sigma }({\mathrm{R}}_{\mathrm{if}},\omega )$ for the isotropic Heisenberg magnet and the $\mathrm{XY}$ magnet of spin-$\frac{1}{2}$ at infinite temperature.