High-Temperature Wavelength-Dependent Properties of a Heisenberg Paramagnet

The first four terms of the high-temperature expansion of the wavelength-dependent susceptibility $\chi \left(\mathbf{k}\right)$ and the spin correlation function $S\left(\mathbf{k}\right)$ are calculated. Nearest-neighbor exchange interactions are assumed with general spin values and a Bravais lattice. From these results the first four terms in the high-temperature expansion of the effective range of the spin correlation are obtained for both ferromagnets and anti-ferromagnets. The terms are slightly different according to whether the range is defined from $\chi \left(\mathbf{k}\right)$ or from $S\left(\mathbf{k}\right)$, though they become identical limitingly close to the critical ordering temperature. The calculated properties can all be measured by current neutron scattering techniques.