Extended universality of the Ising model

Abstract

An extension of the critical-phenomena universality hypothesis assumed previously to be valid for less singular terms is shown to be invalid. A reformulated extension of the universality hypothesis is found to be valid exactly for the spin-1/2 Ising model on the triangular, square, and honeycomb lattices, and, further support is supplied by high- and low-temperature expansions for the susceptibility. The extension fails however for the Ising model on the kagome\r{} lattice and for the spherical model. At present there are insufficient data to test the extended principle for other models or for experimental systems.