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

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