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Parquet equations, describing the competition between superconducting anddensity-wave instabilities, are solved for a three-dimensional isotropic metalin a high magnetic field when only the lowest Landau level is filled. In thecase of a repulsive interaction between electrons, a phase transition to thedensity-wave state is found at finite temperature. In the opposite case ofattractive interaction, no phase transition is found. With decreasingtemperature $T$, the effective vertex of interaction between electronsrenormalizes toward a one-dimensional limit in a self-similar way with thecharacteristic length (transverse to the magnetic field) decreasing as$\ln^{-1/6}(\omega_c/T)$ ($\omega_c$ is a cutoff). Correlation functions havenew forms, previously unknown for conventional one-dimensional orthree-dimensional Fermi-liquids.Comment: 13 pages + 4 figures (included

Metals in a high magnetic field: A universality class of marginal Fermi liquids