Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field

TL;DR

This paper investigates the distribution and nature of Fisher zeros in the complex temperature plane for Q-state Potts models with nonzero magnetic field, revealing critical points, edge singularities, and scaling laws for various Q values.

Contribution

It introduces a detailed analysis of Fisher zeros in the Q-state Potts models under nonzero magnetic field, highlighting physical critical points and edge singularities not present in the Ising case.

Findings

Identification of physical critical points for H_q<0

Determination of Fisher edge singularities for H_q>0

Verification of scaling law for critical exponents

Abstract

The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the $Q>2$ Potts models in the complex temperature plane with nonzero external magnetic field $H_q$. Unlike the Ising model for $H_q\ne0$ which has only a non-physical critical point (the Fisher edge singularity), the $Q>2$ Potts models have physical critical points for $H_q<0$ as well as the Fisher edge singularities for $H_q>0$. For $H_q<0$ the cross-over of the Fisher zeros of the $Q$-state Potts model into those of the ($Q-1$)-state Potts model is discussed, and the critical line of the three-state Potts ferromagnet is determined. For $H_q>0$ we investigate the edge singularity for finite lattices and compare our results with high-field, low-temperature series expansion of Enting. For $3\le Q\le6$ we find that the specific heat, magnetization, susceptibility, and the density of zeros diverge at the Fisher edge singularity with exponents $\alpha_e$, $\beta_e$, and $\gamma_e$ which satisfy the scaling law $\alpha_e+2\beta_e+\gamma_e=2$.