Three-dimensional Heisenberg ferromagnet: A series investigation

Abstract

We present new twelfth-order high-temperature series for the susceptibility, correlation length, and free energy of the nearest-neighbor classical Heisenberg ferromagnet in zero field on a fcc lattice. Checks corroborating the correctness of the series are discussed. Standard analysis of these series produces results in essential agreement with the renormalization-group calculations and several other series analyses. However, a more reliable confluent singularity analysis suggests slightly larger values, γ${=1.40\mathrm{}}_{\mathrm{-}0.01}^{+0.03\mathrm{}}$ and ν=0.72±0.01, as well as a confluent correction of just the size to cause the observed standard analysis underestimate.