High-temperature series for the susceptibility of the spin-sIsing model: Analysis of confluent singularities

We have extended the series for the zero-field susceptibility of the spin-s Ising model through tenth order in the reduced inverse temperature K on the square, triangular, simple-cubic, body-centered-cubic, and face-centered-cubic lattices. The series coefficients hₙ(s) are expressed as simple polynomials in $X=s(s+1)$. Using extended methods of analysis we have estimated the nature of the leading singularities on the face-centered lattice and conclude with good confidence that the susceptibility exponent γ₁ equals 1.25, independent of s. The exponent of the leading correction term is estimated to be γ₂0.75±0.08 in good agreement with renormalization-group theory. For s=1/2 only, the amplitude of the confluent correction apparently vanishes. We have also studied the leading singularities on the triangular lattice and conclude that γ₁=7/4, independent of s, with, however, much stronger corrections than in three dimensions. These results provide a very strong corroboration of the universality hypothesis.