Since four-fermion operators in strongly coupled QED are nonperturbati
vely renormalizable, we analyze here the phase diagram and critical be
haviour of the Gauged Nambu-Jona Lasinio model. Our mean field approxi
mation relates the critical exponents along the continuous phase trans
ition line with the mass dependence of the chiral condensate in the Co
ulomb phase of standard noncompact QED. The numerical results for nonc
ompact QED strongly suggest non mean field exponents along the critica
l line.