Spin-Spin Correlations of the Classical Heisenberg Ferromagnet on the fcc Lattice, for Temperatures aboveTC

High-temperature series are presented for the spin-spin correlation function of the spin-infinity nearest-neighbor Heisenberg ferromagnet on the fcc lattice. Our zero-field series are to tenth order in the interaction, while our finite field series are to eighth order in the interaction. Previous analysis of these series indicated $\gamma =1.405\mathrm{}\pm 0.020$ and $\nu =0.717\mathrm{}\pm 0.007$. These series are used to determine the true correlation length. Further examination of these series indicates that, where the inverse correlation length $\kappa$ is not much smaller than the momentum transfer $\kappa$ (explicitly $\frac{{\kappa }^2}{k^2}>0.08\mathrm{}$, the correlations in momentum space are well represented by the Ornstein-Zernike form ${\mu }^{\eta }(k^2+{\mu }^2)$, where $\eta$ has been found to be 0.040 ± 0.008, not zero as in mean-field theories.