The chiral phase transition of QED$_3$ around the critical number of fermion flavors

TL;DR

This paper investigates the chiral phase transition in QED3 at zero temperature, analyzing how the transition type depends on the fermion flavor number and the vertex approximation used.

Contribution

It compares the nature of the chiral phase transition in QED3 using different vertex approximations through numerical solutions of Dyson-Schwinger equations.

Findings

High-order continuous transition with bare vertex at critical Nf

Second-order transition with simplified Ball-Chiu vertex

Identification of the critical fermion flavor number Nf,c

Abstract

At zero temperature and density, the nature of the chiral phase transition in QED$_3$ with $\textit{N}_{f}$ massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson-Schwinger equations for the fermion and boson propagator within the bare and simplified Ball-Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu-Goldstone phase into the Wigner phase when the number of fermion flavors $\textit{N}_{f}$ reaches the critical number $\textit{N}_{f,c}$, while the system exhibits a typical characteristic of second-order phase transition for the simplified Ball-Chiu vertex.