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

Abstract

High-temperature series expansions for the Ising model's spin-spin correlation function are found to order ${(\frac{J}{\mathrm{kT}})}^{12}$ 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 $\ensuremath{\kappa}r$ fixed, $\ensuremath{\kappa}\ensuremath{\rightarrow}0$. Values are obtained for the correlation indices $\ensuremath{\nu}$ and $\ensuremath{\eta}$-the latter by two methods, thereby providing a direct check on the scaling law.