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The phase diagram of the $(1 + 1)$-dimensional Gross-Neveu model isreanalyzed for (non-)zero chemical potential and (non-)zero temperature withinthe mean-field approximation. By investigating the momentum dependence of thebosonic two-point function, the well-known second-order phase transition fromthe $\mathbb{Z}_2$ symmetric phase to the so-called inhomogeneous phase isdetected. In the latter phase the chiral condensate is periodically varying inspace and translational invariance is broken. This work is a proof of conceptstudy that confirms that it is possible to correctly localize second-orderphase transition lines between phases without condensation and phases ofspatially inhomogeneous condensation via a stability analysis of thehomogeneous phase. To complement other works relying on this technique, thestability analysis is explained in detail and its limitations and successes arediscussed in context of the Gross-Neveu model. Additionally, we presentexplicit results for the bosonic wave-function renormalization in themean-field approximation, which is extracted analytically from the bosonictwo-point function. We find regions -- a so-called moat regime -- where thewave function renormalization is negative accompanying the inhomogeneous phaseas expected.

journal of physics. a, mathematical and theoretical

Detecting inhomogeneous chiral condensation from the bosonic two-point  function in the $(1 + 1)$-dimensional Gross-Neveu model in the mean-field  approximation