Investigation of phase transition in QED3

In this Letter we investigate dynamical mass generation and phase transition in QED3 for number of fermion flavors N=1,2 at finite chemical potential μ under the rainbow approximation of the Dyson-Schwinger equations. Employing three Ansätze of the fermion-photon vertex, we numerically solve the coupled fermion and photon gap equation at zero chemical potential in the Landau gauge. It is found that the fermion and photon propagators in the Nambu-Goldstone (NG) phase and Wigner (WN) phase thus obtained have distinct behaviors. It is expected that the similar result holds for the quark and gluon propagators in QCD. We then derive a model-independent expression for P(μ) (the pressure at finite μ) in QED3. In this expression, P(μ) is the sum of two terms: the first term is the pressure at μ=0 which is a constant; the second term is totally expressed in terms of the fermion propagator at finite chemical potential and contains all the nontrivial μ-dependence. The order parameter for the phase transition between NG phase and WN phase is the difference between the pressure of NG phase and that of WN phase Δ(μ)=PNG(μ)−PWN(μ). By solving the fermion gap equation at finite μ, the numerical results for the order parameter are obtained. The obtained Δ(μ) is a monotonously decreasing function of μ. When μ reaches a critical value μc which is about 0.015 at N=1 and 0.00163 at N=2, Δ(μ) begins to turn from positive to negative, which means the system goes into the deconfined WN phase and chiral symmetry gets restored.