Extended high-temperature series for the classical Heisenberg model in three dimensions

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Abstract
Extended series expansions are derived for the high-temperature susceptibility of the classical Heisenberg model, on three-dimensional lattices. Series coefficients are presented to twelfth order for the simple cubic (SC) and face centred cubic (FCC) lattices and to eleventh order for the body centred cubic (BCC) lattice. The results are in agreement with earlier calculations apart from a small discrepancy at the tenth order on the FCC lattice. Extrapolation studies on the extended series are used to obtain revised estimates for the critical points (Kc) and the susceptibility exponent ( gamma ). On the FCC lattice, the authors also investigate the possibility of a confluent non-analytic correction to the dominant singularity. While the coefficients are consistent with the presence of such a correction term with an exponent ( Delta 1) of 0.55, as predicted by renormalisation group (RG) calculations, the amplitude of the correction term appears to be very small compared with that of the first analytic correction term.