No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions

We present our numerical study of three-dimensional QED with two, four, six and eight flavors of massless two-component fermions using a parity-preserving lattice regularization with Wilson fermions. We study the behavior of low-lying eigenvalues of the massless improved Wilson-Dirac operator as a function of three-dimensional physical volume, after taking the continuum limit at fixed physical volumes. We find the following evidences against the presence of a bilinear condensate: the eigenvalues do not scale as the inverse of the three-dimensional physical volume, and the number variance associated with these eigenvalues does not exhibit ergodic behavior. The inverse participation ratio (IPR) of the associated eigenvectors exhibits a multifractal volume scaling. The relation satisfied by the number variance and IPR suggests critical behavior.