We study the thermodynamics of the (2+1)-dimensional Gross–Neveu model inspired from graphene. We focus on the entropy density of the Gaussian fluctuation beyond the mean field. The full in-medium, momentum-dependent evaluation reveals that the fluctuations give a substantial contribution, even comparable to that of the mean field. We argue that the back-reaction from the fluctuations to the mean field should be included, which reduces the contribution mainly coming from the Landau-damping region. To treat this self-consistently, we use the generalized version of the Beth–Uhlenbeck approach for the entropy density. Compared with the standard Beth–Uhlenbeck formulation, the generalized version suppresses the low-energy contributions while preserving the bound-state effects. To illustrate this, we consider the respective contributions of the bound excitons and unbound fermions to the total entropy. This shows a sharper crossover between the degrees of freedom compared to the standard Beth–Uhlenbeck approach. This behavior is consistent with Mott-transition physics in two-dimensional materials.
Mahato et al. (Thu,) studied this question.