We have used a slightly modified version of Roskies's quadratic map method [Phys. Rev. B 24, 5305 (1981)] to estimate the confluent correction amplitudes for the susceptibility $\ensuremath{\chi}$ and correlation length $\ensuremath{\xi}$ of a model that interpolates between Ising and Gaussian limits. Our best estimates for the corresponding leading exponents are $\ensuremath{\gamma}=1.237\ifmmode\pm\else\textpm\fi{}0.003$, $\ensuremath{\nu}=0.630\ifmmode\pm\else\textpm\fi{}0.003$, and $\ensuremath{\eta}=2\ensuremath{-}\frac{\ensuremath{\gamma}}{\ensuremath{\nu}}=0.036\ifmmode\pm\else\textpm\fi{}0.002$. The correction to scaling amplitude ratio $\frac{B(\ensuremath{\xi})}{B(\ensuremath{\chi})}=0.8\ifmmode\pm\else\textpm\fi{}0.1$ is slightly larger than that predicted from ${\ensuremath{\varphi}}^{4}$ continuum model analysis [M.-c. Chang and A. Houghton, Phys. Rev. Lett. 44, 785 (1980) and C. Bagnuls and C. Bervillier, Phys. Rev. B 24, 1226 (1981)]
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.
High-temperature series for two bcc lattice models which interpolate between the Gaussian (or free-field) model and the
S=21 Ising model are analyzed by partial differential approximants. Series to order 21 in both $x\ensuremath{\propto}\frac{1}{T}$ and the interpolation parameter,
y, yield unbiased estimates for the correction-to-scaling exponent, $\ensuremath{\theta}=0.54\ifmmode\pm\else\textpm\fi{}5$, and the susceptibility exponent, $\ensuremath{\gamma}=1.2385\ifmmode\pm\else\textpm\fi{}15$. The results are universal and agree tolerably with field-theoretic estimates and well with biased, one-variable analyses of general spin Ising models.
The equivalence of the critical behavior of the
d-dimensional Ising model at a finite temperature to that of a
d- 1 dimensional system at zero temperature as a function of a transverse magnetic field is used to calculate the critical exponents for the three-dimensional model by applying the Niemeijer-Van Leeuwen renormalization-group method to the two-dimensional problem.