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We implement an explicit two-loop calculation of the coupling functions andthe self-energy of interacting fermions with a two-dimensional flat Fermisurface in the framework of the field theoretical renormalization group (RG)approach. Throughout the calculation both the Fermi surface and the Fermivelocity are assumed to be fixed and unaffected by interactions. We show thatin two dimensions, in a weak coupling regime, there is no significant change inthe RG flow compared to the well-known one-loop results available in theliterature. However, if we extrapolate the flow to a moderate coupling regimethere are interesting new features associated with an anisotropic suppressionof the quasiparticle weight Z along the Fermi surface, and the vanishing of therenormalized coupling functions for several choices of the external momenta.Comment: 16 pages and 22 figure

Field-theoretical renormalization group for a flat two-dimensional Fermi surface