Non-Fermi liquid in a truncated two-dimensional Fermi surface

Using perturbation theory and the field theoretical renormalization group approach we consider a two-dimensional anisotropic truncated Fermi Surface (FS) with both flat and curved sectors which approximately simulates the "cold" and "hot" spots in the cuprate superconductors. We calculate the one-particle two-loop irreducible functions Gamma((2)) and Gamma((4)) as well as the spin, the charge and pairing response functions up to one-loop order. We find nontrivial infrared stable fixed points and we show that there are important effects produced by the mixing of the existing scattering channels in higher order of perturbation theory. Our results indicate that the "cold" spots are turned into a non-Fermi liquid with divergents partial derivativeSigma(0)/partial derivativep(0) and partial derivativeSigma(0)/partial derivative(p) over bar, a vanishing Z, and either a finite or zero "Fermi velocity" at the FS when the effects produced by the flat portions are taken into account.