Marginal Fermi liquid with a two-dimensional patched Fermi surface

We consider a model composed of Landau quasiparticle states with patched Fe rmi surfaces (FS) sandwiched by states with Bat FS to simulate the "cold" s pot regions in cuprates. We calculate the one-particle irreducible function and the self-energy up to two-loop order. Using renormalization group argu ments, we show that in the forward scattering channel, the renormalized cou pling constant is never infrared stable due to the flat FS sectors. Furthem ore, we show that the self-energy scales with energy as Re Sigma similar to omega ln omega as omega --> 0, and thus the Fermi liquid state within each FS patch is turned into a marginal Fermi liquid.