High-Temperature Expansions for the Spin-½ Heisenberg Model

Abstract

We obtain high-temperature power-series-expansion coefficients for the spin-\textonehalf{} 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 ${10}^{\ensuremath{-}3}$. The critical index for the susceptibility is $\ensuremath{\gamma}=1.43\ifmmode\pm\else\textpm\fi{}0.01$ and the gap parameter $2\ensuremath{\Delta}=3.63\ifmmode\pm\else\textpm\fi{}0.03$ for all three lattices.