We study a generalized version of the Gross-Neveu model in $2+1$ dimensions. The model is inspired from Graphene, which shows a linear dispersion relation near the Dirac points. The phase structure and the thermodynamic properties in the mean field approximation have been studied before. Here, we go beyond the mean field level by deriving a Beth-Uhlenbeck equation for Gaussian fluctuations formulated in phase shift solutions, which we explore numerically, for the first time including their momentum dependence. We discuss the excitonic mass, fluctuation pressure, and phase shifts. The inclusion of momentum dependence in the phase shift shows a significant difference from the Lorentz-boosted version of the phase shift previously used in the literature. We find resurrection of the pseudoscalar bound states at large momentum above Mott temperature and show that the presence of Landau modes significantly contributes to the fluctuation pressure.

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• Bound states in the continuum
• Dynamical phase transitions
• Equations of state
• Excitons
• Lifetimes & widths
• Many-body techniques
• Phase diagrams
• Phase shift
• Spontaneous symmetry breaking
• Mott insulators
• Chiral symmetry
• Mass
• Bosonization
• Finite temperature field theory
• Gross-Neveu model
• Mean field theory
• Path integrals