High-Temperature Expansions for the Spin-½ Heisenberg Model

We obtain high-temperature power-series-expansion coefficients for the spin-{} Heisenberg model for the simple cubic, body-centered cubic, and face-centered cubic lattices. The specific heat is carried to 10 terms; the susceptibility series, to 10 terms for the loose-packed lattices and 9 for the close-packed one. The coefficients of the 4th, 6th, and 8th powers of magnetic field are carried to 8 terms. We analyze these series and conclude that the critical points are 0.5972, 0.3963, and 0.2492, respectively, with an error of perhaps 10^-3. The critical index for the susceptibility is γ=1.43±0.01 and the gap parameter 2Δ=3.63±0.03 for all three lattices.