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

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.