Domain of zeros of the partition function for some magnetic lattice systems

Abstract

A domain D in the complex fugacityplane containing all zeros of the grand canonical partition function is determined for several lattice models using a theorem by Ruelle. In the case of the Ising model for ferromagnetic (FM), antiferromagnetic (AF), and dilute systems exact upper bounds are derived for the critical temperature and the critical magnetic field, and lower bounds for the gap angle for FM and AF systems and the critical magnetic field beyond the tricritical point of dilute FM systems. © 1973 The American Physical Society.