Phase structure of the massive chiral Gross-Neveu model from the Hartree-Fock approach

The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu--Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature, and compared with the one of the discrete chiral Gross-Neveu model. As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.