High-Temperature Series Expansions for a Spin-1 Model of Ferromagnetism

High-temperature series expansions are derived up to terms in $T^{-4\mathrm{}}$ for the dipole and quadrupole susceptibilities for arbitrary lattices. The expansions are evaluated for a spin-1 isotropic Hamiltonian with bilinear and biquadratic pair interactions. We compare the dipole and quadrupole phase transition temperatures determined from these series to those obtained by the molecular-field and constant-coupling approximations. There are large uncertainties in the estimates of the quadrupole transition temperatures because of the few terms in the series.