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

Abstract

At zero temperature and density, the nature of the chiral phase transition in QED${}_3$ with ${\text{N}}_f$ 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 ${\text{N}}_f$ reaches the critical number ${\text{N}}_{f,c}$, while the system exhibits a typical characteristic of second-order phase transition for the simplified Ball-Chiu vertex.

Comments: 9 pages, 9 figures