Confluent singularities and the correction-to-scaling exponent for thed=3fcc Ising model

Abstract

The susceptibility of the spin-$s$ nearest-neighbor fcc Ising model is studied at zero magnetic field by twelve-term high-temperature series. We find that the data near criticality are consistent with $\chi =A\left(s\right)\mathrm{}{t}^{\frac{-5\mathrm{}}{4}}\mathrm{}[1+B(s\left)\mathrm{}{t}^{{\Delta }_1}\right]$, $t=1-\frac{T_c\mathrm{}\left(s\right)\mathrm{}}{T}$. The correction-to-scaling exponent has the universal value ${\Delta }_1=0.50\mathrm{}\pm 0.05$ in good agreement with $\epsilon$-expansion estimates. The confluent amplitude $B\left(s\right)\mathrm{}$ vanishes at $s=\frac{1}{2}$ to within uncertainties. Values of the critical parameters are tabulated for a variety of spins.