Nonperturbative phase boundaries in the Gross-Neveu model from a stability analysis

Two out of three phase boundaries of the 1 + 1 -dimensional Gross-Neveu model in the chiral limit can be obtained from a standard, perturbative stability analysis of the homogeneous phases. The third one separating the massive homogeneous phase from the kink crystal is nonperturbative and could so far only be inferred from the full solution of the model. We show that this phase boundary can also be obtained via a modified stability analysis, based on the thermodynamic potential of a single kink or baryon. The same method works for the massive Gross-Neveu model, so that all phase boundaries of the Gross-Neveu model could have been predicted quantitatively without prior knowledge of the full crystal solution.