No First-Order Phase Transition in the Gross-Neveu Model?

TL;DR

This paper uses a variational approach to study dense matter in the Gross-Neveu model, suggesting the absence of a first-order phase transition and the persistence of symmetry breaking at all densities.

Contribution

It introduces a novel variational ground state that breaks translational invariance and challenges the conventional belief of symmetry restoration via a first-order transition.

Findings

The variational state has lower energy than the Fermi gas at all densities.

The discrete gamma_5 symmetry does not undergo a first-order restoration.

No evidence of a first-order phase transition in the model.

Abstract

Within a variational calculation we investigate the role of baryons for the structure of dense matter in the Gross-Neveu model. We construct a trial ground state at finite baryon density which breaks translational invariance. Its scalar potential interpolates between widely spaced kinks and antikinks at low density and the value zero at infinite density. Its energy is lower than the one of the standard Fermi gas at all densities considered. This suggests that the discrete gamma_5 symmetry of the Gross-Neveu model does not get restored in a first order phase transition at finite density, at variance with common wisdom.