Some Critical Properties of the Nearest-Neighbor, Classical Heisenberg Model for the fcc Lattice in Finite Field for Temperatures Greater thanTC

Using renormalization techniques on the Englert linked-cluster expansion, we have derived high-temperature series for the spin-spin correlation function of the spin-infinity Heisenberg model in finite field. Analysis of our tenth-order zero-field series, which are two terms longer than previous spin-infinity series, favors values of the critical indices $\gamma$, $\nu$, and $-\alpha$ higher than previous spin-infinity work but in closer agreement with spin-½ results. We find $\gamma =1.405\mathrm{}\pm 0.020$, $\nu =0.717\mathrm{}\pm 0.007$, and $\alpha =-0.14\mathrm{}\pm 0.06$. Our finite-field series to eighth order in the interaction and second order in the field allow us to determine the gap index $\Delta$ for the spin-infinity Heisenberg system; we assert $2\Delta =3.54\mathrm{}\pm 0.03$. Our results are compared with experiment and with the predictions of scaling theory.