Using the appropriately generalised finite lattice method, series expansions of the layer ( chi 1 ) and local ( chi 11 ) susceptibilities of the square lattice Ising model have been obtained. They extend existing series by 3 and 13 terms for chi 1 and chi 11 , respectively. Series analysis yields the exponent estimates gamma 1 =1.375+or-0.005 and gamma 11 =0.00+or-0.01, in agreement with scaling predictions. Repetition of the analysis used in the analogous self-avoiding walk problem confirms the breakdown of the renormalisation group scaling relation gamma 11 =v-1 for the square lattice self-avoiding walk problem found in an earlier study.
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 ${\ensuremath{\gamma}}_{1}$ equals 1.25, independent of
s. The exponent of the leading correction term is estimated to be ${\ensuremath{\gamma}}_{2}\ensuremath{\simeq}0.75\ifmmode\pm\else\textpm\fi{}0.08$ in good agreement with renormalization-group theory. For
s=21 only, the amplitude of the confluent correction apparently vanishes. We have also studied the leading singularities on the triangular lattice and conclude that ${\ensuremath{\gamma}}_{1}=\frac{7}{4}$, independent of
s, with, however, much stronger corrections than in three dimensions. These results provide a very strong corroboration of the universality hypothesis.