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 $r\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\kappa}r$ fixed, but is not valid in the (strong) limit $\ensuremath{\kappa}a\ensuremath{\rightarrow}0$, $r\ensuremath{\gg}a$, with $\ensuremath{\kappa}r$ arbitrary.