Spin-Spin Correlation Function of the Three-Dimensional Ising Ferromagnet Above the Curie Temperature

High-temperature series expansions for the Ising model's spin-spin correlation function are found to order ${\left(\frac{J}{\mathrm{kT}}\right)}^{12}$ on the simple cubic, bcc, and fcc latices. Analysis of moment series indicates that the scaling form of the correlation function is correct, at least in the limit $\kappa r$ fixed, $\kappa \to 0$. Values are obtained for the correlation indices $\nu$ and $\eta$-the latter by two methods, thereby providing a direct check on the scaling law.