Abstract
We numerically study models for superconductivity with two interactions: V > due to antiferromagnetic (AF) fluctuations and V < due to phonons, in a weak coupling approach to the high-temperature superconductivity. The nature of the two interactions is considerably different: V > is positive and sharply peaked at (±π,±π) while V < is negative and peaked at (0,0) due to weak phonon screening. The superconductivity is mainly induced by V < . The positive interactionV > (AF) is not effective in superconductivity, but important to give d-wave superconductivity. The gap order parameter Δ(k) is constant (s-wave) at an extremely overdoped region and it becomes anisotropic as doping is reduced. Then there exists a first-order phase transition between anisotropic s-wave and d-wave gaps as doping is reduced further. These results are qualitatively in agreement with preceding works; they should be modified in the strongly underdoped region by the presence of antiferromagnetic pseudogap due to the fluctuations.