On magnetic catalysis in even-flavor QED3

TL;DR

This paper investigates how external magnetic fields influence fermion mass generation in even-flavor QED3, revealing quadratic and logarithmic scaling behaviors at different field strengths through analytic and lattice methods.

Contribution

It provides the first analytic and lattice analysis of magnetic catalysis in QED3, detailing mass scaling behaviors under varying magnetic field strengths.

Findings

Mass increases quadratically with weak magnetic fields.

Mass scales logarithmically with strong magnetic fields.

Lattice calculations confirm the analytic scaling behaviors.

Abstract

In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scaling logarithmically with the external field. We also confirm this type of scaling behavior through quenched lattice calculations using the non-compact version for the gauge field. Both the zero and finite temperature cases are examined. A preliminary study of the fermion condensate in the presence of magnetic flux tubes on the lattice is also included.