Renormalization group flow of quartic perturbations in graphene: Strong coupling and large-Nlimits

Abstract

We explore the renormalization group flow of quartic perturbations in the low-enegy theory of graphene, in the strong Coulomb coupling and large-$N$ limits, where $N$ is the number of fermion flavors. We compute the anomalous dimensions of the quartic couplings $u$ up to leading order in $1∕N$ and find both relevant and irrelevant directions in the space of quartic couplings. We discuss possible phase diagrams and relevance for the physics of graphene.