Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model

TL;DR

This paper uses the functional renormalization group to analyze how an external magnetic field enhances symmetry breaking and induces a spectral gap in the (2+1)-dimensional Gross-Neveu model with Dirac fermions.

Contribution

It provides a quantitative analysis of magnetic catalysis in the 3d Gross-Neveu model using a pointlike truncation within the functional renormalization group framework.

Findings

Magnetic field induces a spectral gap in the fermionic spectrum.

Pointlike operators up to quartic fermionic terms are generated by the magnetic field.

Renormalization group flow offers a simple picture of magnetic catalysis.

Abstract

Magnetic catalysis describes the enhancement of symmetry breaking quantum fluctuations in chirally symmetric quantum field theories by the coupling of fermionic degrees of freedom to a magnetic background configuration. We use the functional renormalization group to investigate this phenomenon for interacting Dirac fermions propagating in (2+1)-dimensional spacetime, described by the Gross-Neveu model. We identify pointlike operators up to quartic fermionic terms that can be generated in the renormalization group flow by the presence of an external magnetic field. We employ the beta function for the fermionic coupling to quantitatively analyze the field dependence of the induced spectral gap. Within our pointlike truncation, the renormalization group flow provides a simple picture for magnetic catalysis.