Composite operator approach to dynamical mass generation in the (2+1)-dimensional Gross-Neveu model

Using a nonperturbative approach based on the Cornwall-Jackiw-Tomboulis (CJT) effective action $Γ(S)$ for composite operators, the phase structure of the simplest massless (2 + 1)-dimensional Gross-Neveu model is investigated. We have calculated $Γ(S)$ in the first order of the bare coupling constant $G$ and have shown that there exist three different specific dependences of $G\equiv G(Λ)$ on the cutoff parameter $Λ$, and in each case the effective action and its stationarity equations have been obtained. The solutions of these equations correspond to the fact that three different masses of fermions can arise dynamically and, respectively, three different nontrivial phases can be observed in the model.

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