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