  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.
