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

TL;DR

This paper demonstrates that all phase boundaries of the 1+1 dimensional Gross-Neveu model can be predicted using a modified stability analysis, including the non-perturbative boundary, without relying on the full solution.

Contribution

The authors introduce a modified stability analysis method that accurately predicts all phase boundaries of the Gross-Neveu model, including non-perturbative ones.

Findings

All phase boundaries can be predicted without the full solution.

The method applies to both chiral and massive Gross-Neveu models.

Non-perturbative phase boundary can be obtained via 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.