High-temperature series for the susceptibility of the spin-SIsing model

We have extended the series for the zero-field susceptibility of the spin-$S$ Ising model to eighth order in the reduced temperature $K$, on the triangular, simple cubic, body-centered-cubic, and face-centered-cubic lattices. The coefficients of these series $h_n\mathrm{}\left(S\right)\mathrm{}$ are expressed as simple polynomials in $X=S(S+1\mathrm{})\mathrm{}$. For the face-centered-cubic lattice, an accurate polynomial fit to the critical point $K_c\mathrm{}\left(S\right)\mathrm{}$ is presented; and the apparent spin dependence of the critical exponent $\gamma$ is briefly discussed. The series are quite well behaved for all $S$. However, the large-$S$ series seems to exhibit more rapid apparent convergence.