Finite volume effects and dynamical chiral symmetry breaking in QED3

TL;DR

This paper studies how finite volume effects influence the critical number of flavors for chiral symmetry restoration in QED3, revealing significant volume dependence that explains previous discrepancies between continuum and lattice results.

Contribution

It provides a detailed analysis of finite volume effects on N_f^c in QED3 using Dyson-Schwinger equations, clarifying discrepancies in earlier studies.

Findings

Finite volume significantly affects N_f^c estimates.

N_f^c shifts from about 3.7 in infinite volume to below 1.5 at finite volume.

Results align with earlier simplified truncation studies.

Abstract

We investigate the impact of finite volume effects on the critical number of flavours, 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 \le N_f^c \le 3.84 in the infinite volume/continuum limit down to values below N_f \le 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.