PARQUET SOLUTION FOR A FLAT FERMI-SURFACE

We study instabilities occurring in the electron system whose Fermi su rface has flat regions on its opposite sides. Such a Fermi surface res embles Fermi surfaces of some high-T-c superconductors. In the framewo rk of the parquet approximation, we classify possible instabilities an d derive renormalization-group equations that determine the evolution of corresponding susceptibilities with decreasing temperature. Numeric al solutions of the parquet equations are found to be in qualitative a greement with a ladder approximation. For the repulsive Hubbard intera ction, the antiferromagnetic (Spin-density-wave) instability dominates , but when the Fermi surface is not perfectly flat, the d-wave superco nducting instability takes over.