Marginal Fermi Liquid Behaviour in the d = 2 Hubbard Model with Cut-Off

We consider the half-filled Hubbard model with a cut-off forbidding momenta close to the angles of the square shaped Fermi surface. By renormalization group methods we find a convergent expansion for the Schwinger function up to exponentially small temperatures. We prove that the system is not a Fermi liquid, but on the contrary it behaves like a Marginal Fermi liquid, a behaviour observed in the normal phase of high T_c superconductors.