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

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.