Phase transitions and the distribution of temperature zeros of the partition function

Abstract

A general method is given by which the density of complex temperature zeros of the canonical partition function, characterizing the temperature behaviour of a many particle system, can be calculated if only line densities occur. As a result it is shown that straight lines of zeros and a simple power law for the line density form a necessary and sufficient description for equal critical indices α=α′. The most important conclusion is that different critical indices α≡α′ occur if and only if the line of zeros ∁ cuts the real axis under a certain limiting angle. The difference α—α′ is determined by the curvature of ∁