  A model is introduced describing the interplay between superconductivity and
spin-ordering. It is characterized by on-site repulsive electron-electron
interactions, causing antiferromagnetism, and nearest-neighbor attractive
interactions, giving rise to d-wave superconductivity. Due to a special choice
for the lattice, this model has a strong-coupling limit where the
superconductivity can be described by a bosonic theory, similar to the strongly
coupled negative U Hubbard model. This limit is analyzed in the present paper.
A rich mean-field phase diagram is found and the leading quantum corrections to
the mean-field results are calculated. The first-order line between the
antiferromagnetic- and the superconducting phase is found to terminate at a
tricritical point, where two second-order lines originate. At these lines, the
system undergoes a transition to- and from a phase exhibiting both
antiferromagnetic order and superconductivity. At finite temperatures above the
spin-disordering line, quantum-critical behavior is found. For specific values
of the model parameters, it is possible to obtain SO(5) symmetry involving the
spin- and the phase-sector at the tricritical point. Although this symmetry is
explicitly broken by the projection to the lower Hubbard band, it survives on
the mean-field level, and modes related to a spontaneously broken SO(5)
symmetry are present on the level of the random phase approximation in the
superconducting phase.
