Critical number of fermions in three-dimensional QED

Previous analytical studies of quantum electrodynamics in $2+1$ dimensions (QED3) have shown the existence of a critical number of fermions for onset of chiral symmetry breaking, the most known being the value Nc≈3.28 obtained by Nash to 1/N² order in the $1/N$ expansion [D. Nash, Phys. Rev. Lett. 62, 3024 (1989)]. This analysis is reconsidered by solving the Dyson-Schwinger equations for the fermion propagator and the vertex to show that the more accurate gauge-independent value is Nc≈2.85, which means that the chiral symmetry is dynamically broken for integer values N≤2, while for N≥3 the system is in a chirally symmetric phase. An estimate for the value of chiral condensate ⟨ψψ⟩ is given for $N=2$. Knowing precise Nc would be important for comparison between continuum studies and lattice simulations of QED3.