Scaling Form of the Spin-Spin Correlation Function of the Three-Dimensional Ising Ferromagnet above the Curie Temperature

Abstract

The spin-spin correlation function for the $S=\frac{1}{2}$ Ising ferromagnet is evaluated in zero magnetic field and for $T>~T_c$ by the method of series expansions. Evidence is presented showing that the scaling of correlations is valid in the (weak) limit $r\to \infty$, $\kappa r$ fixed, but is not valid in the (strong) limit $\kappa a\to 0$, $r\gg a$, with $\kappa r$ arbitrary.