No first-order phase transition in the Gross-Neveu model?

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.