Upper bounds on critical temperature and magnetic field for a class of Ising spin-1 models

Abstract

Regions in the complex ${e}^{\ensuremath{\beta}h}$ plane ($\ensuremath{\beta}$ is the inverse temperature, $h$ is the magnetic field) containing zeros of the partition function are determined for two spin-1 Ising systems. The models considered are (1) the dilute Ising model and (2) an Ising-model analog to a binary-lattice gas. The models are first converted into analog spin-1/2 systems using a transformation due to Griffiths. Regions containing the zeros of the partition functions are then determined by use of a theorem established by Ruelle. For model (1) we obtain bounds on the critical temperature and critical magnetic field. For model (2) a condition for the zeros to lie on the unit circle is determined.