Many-flavor phase diagram of the (2+1)d Gross-Neveu model at finite temperature

We study the phase diagram of the Gross-Neveu model in d = 2+ 1 space-time dimensions in the plane spanned by temperature and the number of massless fermion flavors. We use a functional renormalization group approach based on a nonperturbative derivative expansion that accounts for fermionic as well as composite bosonic fluctuations. We map out the phase boundary separating the ordered massive low-temperature phase from the disordered high-temperature phase. The phases are separated by a second-order phase transition in the 2d Ising universality class. We determine the size of the Ginzburg region and show that it scales to zero for large N-f following a powerlaw, in agreement with large-N-f and lattice studies. We also study the regimes of local order above as well as the classical regime below the critical temperature. Our results could be of interest for the finite-temperature behavior of condensed-matter realizations of Dirac fermions, as e.g. electrons on the graphene honeycomb with a short-range interaction.