Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series

We have extended through β²³ the high-temperature expansion of the second field derivative of the susceptibility for Ising models of general spin, with nearest-neighbor interactions, on the simple cubic and the body-centered cubic lattices. Moreover, the expansions for the nearest-neighbor correlation function, the susceptibility, and the second correlation moment have been extended up to β²⁵. Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyperuniversal combinations of critical amplitudes such as the renormalized four-point coupling gᵣ or the quantity usually denoted by R_ξ⁺. In particular, we obtain γ=1.2371(1), ν=0.6299(2), γ₄=4.3647(20), gᵣ=1.404(3), and R_ξ⁺=0.2668(5). We have used a variety of series extrapolation procedures and, in some of the analyses, we have assumed that the leading correction-to-scaling exponent θ is universal and roughly known. We have also verified, to high precision, the validity of the hyperscaling relation and of the universality property both with regard to the lattice structure and to the value of the spin.