Zeros of the grand canonical partition function: Generalization of a result of Lee and Yang

Abstract

A simple sufficiency condition for the zeros of a polynomial of grand partition function form to lie entirely on the unit circle in the complex fugacity (z) plane is rigorously proven. The condition has two parts: the canonical partition function Qn(M) is symmetric, Qn(M) =QM−n(M), and is bounded above by the binomial coefficient (Mn). This represents a generalization of the condition given by Lee and Yang in the context of the Ising model and the proof is independent of theirs. Necessity of the condition is trivially proven.