High-temperature series for the spin-one Ising model for arbitrary biquadratic exchange, field, and anisotropy

The spin-one Ising system $-\beta \mathcal{H}=K\Sigma {〈i,j〉}^{}(S_i{S}_j+\eta S_i^2{S}_j^2)+\Sigma k^{}(h{S}_k+\Lambda S_k^2)$ is considered. We have obtained high-temperature series for the free energy through eighth order for arbitrary $\eta$, $h$, and $\Lambda$ by rewriting this Hamiltonian in a form which exploits its relation to the three-component Potts model ($\eta =3\mathrm{}$). Explicit results are presented for the bcc lattice.