Department of Physics2024-11-1020020001-873210.1080/000187302101551422-s2.0-0036865119http://dx.doi.org/10.1080/00018730210155142https://hdl.handle.net/20.500.14288/16371The numerical studies of d(x2-y2)-wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high-T-c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d(x2-y2)-wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t-J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at (pi,pi) momentum transfer, and enhanced single-particle spectral weight near the (pi,0) and (0,pi) points of the Brillouin zone, create optimum conditions for d(x2)-(y2)-wave pairing. These are two effects which act to enhance the d(x2-y2)-wave pairing correlations in the Hubbard model. Finding additional ways is an active research problem.PhysicsCondensed matterReview1460-6976179448200002Q11156