The two-dimensional spin-1 Ising system and related models

Publisher Website
Google Scholar
Abstract
Although the two-dimensional spin-1/2 Ising model was solved in zero field in 1944, no exact results are yet available for the spin-1 model. This model should have the same dominant critical exponents as the spin-1/2 model, but appears to exhibit non-analytic corrections to scaling as expected for a phi 4 model and unlike the spin-1/2 model. In this paper new 45-term low temperature series for the magnetisation, specific heat and susceptibility of the spin-1 model on the square lattice are presented and analysed. A new 24-term staggered susceptibility series for the hard square model is presented and the extant order parameter series for this model (which is also in the phi 4 universality class) are also considered. For both models a non-analytic confluent correction with exponent 1.0< Delta 11/2 case.