Critical behaviour of ($2+1$)-dimensional QED: 1/N_f-corrections in the Landau gauge

TL;DR

This paper investigates the critical behavior of (2+1)-dimensional QED, analyzing how fermion mass generation depends on the number of fermion flavors with 1/N corrections in the Landau gauge, finding a small correction to the critical flavor number.

Contribution

It provides a detailed calculation of 1/N_f corrections to the critical fermion flavor number in (2+1)-dimensional QED within the Landau gauge, refining previous leading-order results.

Findings

Critical fermion flavor number N_c = 3.29

Dynamical mass appears for N < N_c

1% correction to leading order value

Abstract

The dynamical generation of a fermion mass is studied within ($2+1$)-dimensional QED with $N$ four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, N_c. It is found that the dynamical fermion mass appears for N<N_c where N_c=3.29, that is only about $1\%$ larger than its value at leading order.