Abstract
In order to investigate possible nonphonon mechanisms for superconductivity in the copper oxide compounds, the two-dimensional Hubbard model is studied in the weak-coupling limit. A scaling theory is developed which allows a consistent treatment of the coupled ln2(T)-singularities arising from density wave and Cooper pairing fluctuations. For a half-filled band a spin-density-wave (antiferromagnetic) phase transition occurs, whereas for small deviations from half-filling spin fluctuations lead to a d-type superconducting phase. The method generalizes straightforwardly to finite-range interactions. The possible relevance to oxide superconductors and experimental tests are briefly discussed.