Thermopower near a critical point

Previous calculations of the effect of a critical point on the thermopower of metallic ferromagnets are extended to include inelastic scattering processes. Denoting the (temperature-dependent) localized spin-spin correlation function by $g_{\overrightarrow{\mathrm{k}}}\left(\omega \right)$, where $\overrightarrow{\mathrm{k}}$ is the momentum transfer, and $\omega$ the frequency transfer, the thermopower is shown to be proportional to frequency integrals of $g_{{2k}_F}\left(\omega \right)$ and frequency and wave-vector integrals of $k{g}_{\overrightarrow{\mathrm{k}}}\left(\omega \right)$. Only if the spin-spin correlation function exhibits critical "slowing down" for all frequencies at all $\overrightarrow{\mathrm{k}}\text{'}\mathrm{s}$ (an unlikely prospect) does our result reduce to those found previously.