The Gross-Neveu model on a sphere with a magnetic monopole

TL;DR

This paper presents an exact solution for the phase structure of the Gross-Neveu model on a sphere with a magnetic monopole, revealing how magnetic fields influence chiral symmetry breaking and phase transitions.

Contribution

The study provides the first exact solution for the effective potential of the Gross-Neveu model under combined gravitational and magnetic fields, enabling detailed phase diagram analysis.

Findings

Small magnetic fields may induce second order phase transitions.

Strong magnetic fields favor chiral symmetry breaking.

Magnetic fields prevent decay of the chiral condensate.

Abstract

We study, for the first time, the phase structure of the Gross--Neveu model with a combination of a (constant) gravitational and a magnetic field. This has been made possible by our finding of an exact solution to the problem, namely the effective potential for the composite fermions. Then, from the corresponding implicit equation the phase diagram for the dynamical fermion mass is calculated numerically for some values of the magnetic field. %(what can be done with arbitrary precision). For a small magnetic field the phase diagram hints to the possibility of a second order phase transition at some critical curvature. With growing magnetic field only the phase with broken chiral symmetry survives, because the magnetic field prevents the decay of the chiral condensate. This result is bound to have important consequences in early universe cosmology.