Yang-Lee zeros of the one-dimensional Q-state Potts model

TL;DR

This paper investigates the distribution of Yang-Lee zeros in one-dimensional Q-state Potts models, revealing diverse patterns and the presence of zeros on the positive real axis for both ferromagnetic and antiferromagnetic cases across various Q and temperature values.

Contribution

It provides the first comprehensive analysis of Yang-Lee zeros in the 1D Q-state Potts antiferromagnet for arbitrary Q and temperature, uncovering new zero distributions.

Findings

Zeros on positive real axis for Q<1 in ferromagnetic case

Zeros on positive real axis for both Q<1 and Q>1 in antiferromagnetic case

Diverse shapes of Yang-Lee zero distributions

Abstract

The distributions of the Yang-Lee zeros of the ferromagnetic and antiferromagnetic Q-state Potts models in one dimension are studied for arbitrary Q and temperature. The Yang-Lee zeros of the Potts antiferromagnet have been fully investigated for the first time. The distributions of the Yang-Lee zeros show a variety of different shapes. Some of the Yang-Lee zeros lie on the positive real axis even for T>0. For the ferromagnetic model this happens only for Q<1, while there exist some zeros of the antiferromagnetic model on the positive real axis both for Q<1 and for Q>1.