High-temperature-series study of the spin-½ Heisenberg ferromagnet

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Abstract
We have extended existing high-temperature-series expansions for the spin-½ Heisenberg ferromagnet, for both the zero-field free energy and susceptibility. Series are obtained to order 13 for the simple cubic and body-centered cubic lattices and to order 12 for the face-centered cubic lattice, an addition of three terms in each case. The series are analyzed by a battery of methods and more precise estimates of the critical temperatures and exponents obtained. We also obtain estimates of the specific heat and susceptibility of the standard two- and three-dimensional lattices as functions of temperature, in the high-temperature region.