We study instabilities occurring in the electron system whose Fermi surface has flat regions on its opposite sides. Such a Fermi surface resembles Fermi surfaces of some high-Tc superconductors. In the framework of the parquet approximation, we classify possible instabilities and derive renormalization-group equations that determine the evolution of corresponding susceptibilities with decreasing temperature. Numerical solutions of the parquet equations are found to be in qualitative agreement with a ladder approximation. For the repulsive Hubbard interaction, the antiferromagnetic (spin-density-wave) instability dominates, but when the Fermi surface is not perfectly flat, the d-wave superconducting instability takes over. 74.25.Dw, 75.30.Fv

ac and dc magnetotransport data in the normal state of YBa2Cu3O7 are analyzed within Fermiliquid and non-Fermi-liquid models. In the Fermi-liquid analysis we use the Fermi surface deduced from band-structure calculations and angular-resolved photoemission experiments and assume that the electron relaxation rate varies over the Fermi surface. The non-Fermi-liquid models are the two-dimensional Luttinger liquid model and the charge-conjugation-symmetry model. We find that the existing experimental data can be adequately fit by any of these models. This work provides a framework for the analysis of experiments that may discriminate among these models. 74.25.Gz, 74.25.Fy,

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We develop a systematic theory of the Hall effect in Q1D conductors in both weak and strong magnetic fields for a model where the electron relaxation time varies over the Fermi surface. At high temperatures, the Hall coefficient saturates at the value −β/ecn, where the dimensionless coefficient β is determined by the curvature of the longitudinal dispersion law of electrons, e the electron charge, c is the speed of light, and n is the hole concentration. At low temperatures, where a strong variation of the relaxation rate over the Fermi surface develops in the form of "hot spots", the Hall coefficient becomes temperature-dependent and may change sign for a particular choice of the transverse dispersion law parameters. In our model, the sign changes in a weak, but not in a strong magnetic field.