Title: Rigorous construction of ground state correlations for the 2D Hubbard model on the honeycomb lattice Author: Vieri Mastropietro Abstract: We consider the 2D Hubbard model on the honeycomb lattice, as a model for graphene; at half filling and weak short range 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 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. Partial results for the case of long range Coulomb interactions will be also presented. Results in collaboration with A. Giuliani. Reference: Phys. Rev. B 79, 201403(Rapid Comm.) (2009)