Magnetic catalysis in the $1$-flavor Gross-Neveu model in $2+1$ dimensions

TL;DR

This study uses lattice simulations to demonstrate magnetic catalysis in the 2+1 dimensional Gross-Neveu model, showing an increase in chiral condensate with magnetic field below the phase transition, consistent with theoretical predictions.

Contribution

First lattice simulation evidence of magnetic catalysis in the 2+1D Gross-Neveu model using overlap fermions.

Findings

Chiral condensate increases with magnetic field below transition

Magnetic catalysis observed across all temperatures below phase transition

Results align with mean-field and beyond-mean-field theories

Abstract

We investigate the Gross-Neveu model in $2+1$ dimensions in a constant and homogeneous magnetic field using one reducible flavor of overlap fermions. Our lattice simulations suggest that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, is present for all temperatures below the chiral phase transition, in accordance with predictions from mean-field and beyond-mean-field calculations.