Some Critical Properties of the Nearest-Neighbor, Classical Heisenberg Model for the fcc Lattice in Finite Field for Temperatures Greater than TC
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 γ, ν, and -α higher than previous spin-infinity work but in closer agreement with spin- 1/2 results. We find γ=1.405+/-0.020, ν=0.717+/-0.007, and α=-0.14+/-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 ∆ for the spin-infinity Heisenberg system; we assert 2∆=3.54+/-0.03. Our results are compared with experiment and with the predictions of scaling theory.