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

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