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

Abstract

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 $h_n\mathrm{}\left(s\right)\mathrm{}$ are expressed as simple polynomials in $X=s\mathrm{}(s+1\mathrm{})\mathrm{}$. 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 ${\gamma }_1$ equals 1.25, independent of $s$. The exponent of the leading correction term is estimated to be ${\gamma }_2\simeq 0.75\pm 0.08$ in good agreement with renormalization-group theory. For $s=\frac{1}{2}$ only, the amplitude of the confluent correction apparently vanishes. We have also studied the leading singularities on the triangular lattice and conclude that ${\gamma }_1=\frac{7}{4}$, independent of $s$, with, however, much stronger corrections than in three dimensions. These results provide a very strong corroboration of the universality hypothesis.