Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models

TL;DR

This paper investigates the phase transitions of infinite-range two- and three-state Potts models by analyzing Yang-Lee zeros, revealing critical points, phase regimes, and deriving transition lines.

Contribution

It provides a detailed analysis of Yang-Lee zeros in the Potts models, identifying tricritical points and phase regimes with exact transition line expressions.

Findings

Identification of the tricritical point via zeros approaching the real axis

Scaling properties reveal different phase transition regimes

Exact expression for the transition line at negative fields

Abstract

The phase diagram of the two- and three-state Potts model with infinite-range interactions, in the external field is analyzed by studying the partition function zeros in the complex field plane. The tricritical point of the three-state model is observed as the approach of the zeros to the real axis at the nonzero field value. Different regimes, involving several first- and second-order transitions of the complicated phase diagram of the three state model are identified from the scaling properties of the zeros closest to the real axis. The critical exponents related to the tricritical point and the Yang-Lee edge singularity are well reproduced. Calculations are extended to the negative fields, where the exact implicit expression for the transition line is derived.