Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature

Abstract

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 $\Nf$ following a powerlaw, in agreement with large-$\Nf$ and lattice studies. We also study the regimes of local order above as well as the classical regime below the critical temperature.

16 pages, 7 figures

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• Scale symmetry breaking and generation of mass at quantum critical points
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• Spontaneous symmetry breaking of $\mathrm{SO}(2N)$ in Gross--Neveu theory from $2+\epsilon$ expansion