High-Temperature Expansions for the Classical Heisenberg Model. II. Zero-Field Susceptibility

The high-temperature series expansion of the zero-field magnetic susceptibility, {₂ₔₑ₈₄}=1+l=1^a₋ (J{kT) }^l, is related to the diagrammatic representation of the corresponding high-temperature expansion of the zero-field static spin correlation function 〈{S₅S₆〉}_ presented elsewhere. The first nine terms a₋ for loose-packed lattices and the first seven terms for close-packed lattices in the susceptibility series are explicitly obtained in terms of Domb's "general lattice constants" p₋ₗ. The general lattice expressions are then used to evaluate these a₋ numerically for three two-dimensional lattices and for three cubic lattices. Finally, the a₋ are employed to discuss two questions of current interest: (1) Does the critical exponent ---in the assumed form of the divergence of, (T-{T₂) }^- as T{T₂}^+---have the value 43 for the fcc, bcc, and sc lattices? (2) Do high-temperature expansions suggest a phase transition (T₂0) for some two-dimensional lattices with nearest-neighbor ferromagnetic interactions? It is argued that extrapolation suggests is definitely greater than 43 for the fcc, bcc, and sc lattices, and that T₂ is appreciably different from zero for the plane square and triangular lattices.