Renormalization group analysis of electrons near a Van Hove singularity.

A model of interacting two dimensional electrons near a Van Hove singularity is studied, using renormalization group techniques. In hole doped systems, the chemical potential is found to be pinned near the singularity, when the electron-electron interactions are repulsive. The RG treatment of the leading divergences appearing in perturbation theory give rise to marginal behavior and anisotropic superconductivity.Comment: 4 Latex pages + 5 postcript figure

Electrostatic screening in fullerene molecules

The screening properties of fullerene molecules are described by means of a continuum model which uses the electronic wavefunctions of planar graphite as a starting point. The long distance behavior of the system gives rise to a renormalizable theory, which flows towards a non trivial fixed point. Its existence implies an anomalous dielectric constant. The screening properties are neither metallic nor insulating. Alternatively, the intramolecular screening is obtained from a simple approximation to the electronic wavefunctions. Intermolecular effects are also calculated. As a consistency check, it is shown that the observed polarizability of C$_{60}$ is well eproduced.Comment: 7 pages. Revte