Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)--\ensuremath{\delta}(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.
The interplay between antiferromagnetism and superconductivity is studied by using the three-dimensional nearly half-filled Hubbard model with anisotropic transfer matrices
tz and ${t}_{\ensuremath{\perp}}.$ The phase diagrams are calculated for varying values of the ratio ${r}_{z}{=t}_{z}{/t}_{\ensuremath{\perp}}$ using the spin fluctuation theory within the fluctuation-exchange approximation. The antiferromagnetic phase around the half-filled electron density expands while the neighboring phase of the anisotropic ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductivity shrinks with increasing
rz. For small
rz Tc decreases slowly with increasing
rz. For moderate values of
rz we find a second order transition, with lowering temperature, from the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconducting phase to a phase where an incommensurate spin density wave (SDW) coexists with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductivity. Resonance peaks discussed previously for two-dimensional (2D) superconductors are shown to survive in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconducting phase of 3D systems. Soft components of the incommensurate SDW spin fluctuation mode grow as the coexistent phase is approached.