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

The high-temperature series expansion of the zero-field magnetic susceptibility, χχCurie=1+Σl=1^∞aₗ(J/kT)ˡ, is related to the diagrammatic representation of the corresponding high-temperature expansion of the zero-field static spin correlation function 〈Sf·Sg〉_β presented elsewhere. The first nine terms aₗ 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" pₗₓ. The general lattice expressions are then used to evaluate these aₗ numerically for three two-dimensional lattices and for three cubic lattices. Finally, the aₗ are employed to discuss two questions of current interest: (1) Does the critical exponent γ---in the assumed form of the divergence of χ, χ~(T-Tc)^-γ as T→Tc⁺---have the value 4/3 for the fcc, bcc, and sc lattices? (2) Do high-temperature expansions suggest a phase transition (Tc≠0) for some two-dimensional lattices with nearest-neighbor ferromagnetic interactions? It is argued that extrapolation suggests γ is definitely greater than 4/3 for the fcc, bcc, and sc lattices, and that Tc is appreciably different from zero for the plane square and triangular lattices.