Partition function zeros of the Q-state Potts model on the simple-cubic lattice

TL;DR

This paper investigates the distribution of partition function zeros of the Q-state Potts model on a simple-cubic lattice, analyzing critical behavior and singularities in complex temperature and magnetic field planes through series expansions.

Contribution

It provides a detailed analysis of the zeros' distribution and estimates critical exponents at complex-temperature and Fisher edge singularities, extending understanding of phase transitions in three dimensions.

Findings

Distribution of zeros reveals critical behavior in ferromagnetic and antiferromagnetic phases.

Characteristic exponents at complex-temperature singularities are estimated.

Fisher edge singularities are related to Yang-Lee edge singularities.

Abstract

The $Q$-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on the distribution of the zeros in the complex temperature plane. The characteristic exponents at complex-temperature singularities, which coexist with the physical critical points in the complex temperature plane for no magnetic field ($H_q=0$), are estimated using the low-temperature series expansion. We also study the partition function zeros of the Potts model for nonzero magnetic field. For $H_q>0$ the physical critical points disappear and the Fisher edge singularities appear in the complex temperature plane. The characteristic exponents at the Fisher edge singularities are calculated using the high-field, low-temperature series expansion. It seems that the Fisher edge singularity is related to the Yang-Lee edge singularity which appears in the complex magnetic-field plane for $T>T_c$.