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

TL;DR

This study extends high-temperature series for Ising models of various spins on cubic lattices, improving estimates of critical exponents and universal amplitude ratios, and confirms hyperscaling and universality with high precision.

Contribution

Extended high-temperature series for Ising models of general spin, enabling more accurate critical exponent and amplitude ratio estimates, and validated hyperscaling and universality.

Findings

Improved critical exponent estimates

Validated hyperscaling relation

Confirmed universality across lattice types and spins

Abstract

We have extended through beta^{23} 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 beta^{25}. Taking advantage of these new data, we can improve the accuracy of direct estimates of critical exponents and of hyper-universal combinations of critical amplitudes such as the renormalized four-point coupling g_r or the quantity usually denoted by R^{+}_{xi}. 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 theta 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.