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We consider the 2D Hubbard model on the honeycomb lattice, as a model forsingle layer graphene with screened Coulomb interactions; at half filling andweak coupling, we construct its ground state correlations by a convergentmultiscale expansion, rigorously excluding the presence of magnetic orsuperconducting instabilities or the formation of a mass gap. The Fermivelocity, which can be written in terms of a convergent series expansion,remains close to its non-interacting value and turns out to be isotropic. Onthe contrary, the interaction produces an asymmetry between the two componentsof the charge velocity, in contrast with the predictions based on relativisticor continuum approximations.

Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities