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

Abstract

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 non-perturbative 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.

Comments: 16 pages, 14 figures; v2: analytical proof of self-consistency completed, typos in Eqs. 34 and 44 corrected, reference added