Finite-volume effects and dynamical chiral symmetry breaking in QED₃

We investigate the impact of finite-volume effects on the critical number of flavors, N_f^c, for chiral symmetry restoration in QED₃. To this end we solve a set of coupled Dyson-Schwinger equations on a torus. For order parameters such as the anomalous dimension of the fermion wave function or the chiral condensate, we find substantial evidence for a large dependence on the volume. We observe a shift in N_f^c from values in the range of 3.61≤N_f^c≤3.84 in the infinite-volume and continuum limit down to values below N_f≤1.5 at finite volumes in agreement with earlier results of Gusynin and Reenders in a simpler truncation scheme. These findings explain discrepancies in N_f^c between continuum and lattice studies.