Nonperturbative infrared dynamics of three-dimensional QED with a   four-fermion interaction
  A non-linear Schwinger-Dyson (SD) equation for the gauge boson propagator of massless QED in one time and two spatial dimensions is studied. It is shown that the nonperturbative solution leads to a nontrivial renormalization-group infrared fixed point quantitatively close to the one found in the leading order of the 1/N expansion, with N the number of fermion flavors. In the gauged Nambu-Jona-Lasinio (GNJL) model an equation for the Yukawa vertex is solved in an approximation given by the one-photon exchange and an analytic expression is derived for the propagator of the scalar fermion-antifermion composites. Subsequently, the mass and width of the scalar composites near the phase transition line are calculated as functions of the four-fermion coupling g and flavor number N. The possible relevance of these results for describing particle-hole excitations, in particular antiferromagnetic correlations, observed in the underdoped cuprates, is briefly discussed. 
Valery Gusynin, Anthony Hams, Manuel Reenders