Non-Compact QED_3 with N_f=1 and N_f=4

TL;DR

This paper presents numerical evidence that chiral symmetry is spontaneously broken in non-compact QED_3 with N_f=1, estimates the condensate, and compares N_f=1 and N_f=4 to explore the critical flavor number for symmetry breaking.

Contribution

It provides the first numerical analysis of chiral symmetry breaking in non-compact QED_3 for N_f=1 and 4, estimating the condensate and analyzing phase transition behavior.

Findings

Chiral symmetry is spontaneously broken for N_f=1.

Estimated condensate magnitude is approximately 10^-3.

Difficulty in determining whether N_f=4 is above or below the critical flavor number.

Abstract

We present numerical results for non-compact three-dimensional QED for numbers of flavors N_f=1 and N_f=4.In particular, we address the issue of whether chiral symmetry is spontaneously broken in the continuum limit, and obtain a positive answer for N_f=1, with a dimensionless condensate estimated to be beta^2<psibarpsi> ~= O(10^-3), implying that the critical number of flavors N_fc>1. We also compare the N_f=1 and N_f=4 models by analysing the transition from strong to weak coupling behaviour using an equation of state based on a continuous phase transition. While some qualitative differences emerge, it appears difficult to determine whether N_f=4 lies above or below N_fc.