TOWARDS THE CHIRAL LIMIT OF STRONGLY COUPLED QUENCHED QED

Chiral symmetry breaking in quenched non-compact lattice QED is studied using the Lanczos and conjugate-gradient algorithms on lattices ranging in size from 84 to 324. We find a phase transition at βc = 1/ε{lunate}2 = 0.26-0.27 which is not described by mean field theory, supporting the notion that this model defines an interacting strongly coupled field theory. The finite-size effects and systematic errors in both algorithms are studied in quantitative detail. In the immediate vicinity of the phase transition, estimates of the chiral condensate are sensitive to the procedure for extracting the density of eigenvalues ρ{variant}(0) in the Lanczos case and the zero fermion-mass extrapolation technique of the conjugate-gradient algorithm. In the Lanczos case, if we extract ρ{variant}(0) by the same procedure as used in quenched non-abelian studies, the chiral condensate is well fitted by the essential singularity proposed by Miransky. However, the apparent lack of finite-size effects in quenched QED as compared to the non-abelian models makes this procedure seemingly arbitrary. © 1990.