  We present numerical evidences using overlap fermions for a scale-invariant
behavior of parity-invariant three-dimensional QED with two flavors of massless
two-component fermions. Using finite-size scaling of the low-lying eigenvalues
of the massless anti-Hermitian overlap Dirac operator, we rule out the presence
of bilinear condensate and estimate the mass anomalous dimension. The
eigenvectors associated with these low-lying eigenvalues suggest critical
behavior in the sense of a metal-insulator transition. We show that there is no
mass gap in the scalar and vector correlators in the infinite volume theory.
The vector correlator does not acquire an anomalous dimension. The anomalous
dimension associated with the long-distance behavior of the scalar correlator
is consistent with the mass anomalous dimension.
