Longitudinal Correlation Function of the Heisenberg Ferromagnet

The correlation function of the $z$ components (parallel to the net magnetization) of two spins in a Heisenberg ferromagnet is computed by a Green function analysis. The results extend spin-wave theory to higher temperatures, although they are not satisfactory near the Curie temperature. The Fourier transform of the correlation function varies as $\frac{1}{k}$ for small $k$, with a more complicated behavior at large $k$.