Ising model amplitudes and extended lattice-lattice scaling

Abstract

Extended lattice-lattice scaling (that is, universality of scaling corrections) is investigated for the two- and three-dimensional Ising models. It is shown to break down for non-Archimedean lattices in two dimensions, and for all lattices in three dimensions. In the course of the investigation several new higher order amplitudes for the two- and three-dimensional Ising models are obtained. These include an exact evaluation of the amplitude of the second most singular term of the susceptibility of the Kagome lattice, for which we find C1+=0.086936625, C1-=-0.0023063996.