  The interplay between antiferromagnetism and d-wave superconductivity is
studied in a mean-field approximation for a generic microscopic Hamiltonian
with short-range repulsion and near-neighbor attraction. In the presence of
competing microscopic interactions, the phase boundaries of antiferromagnetic
and superconducting states are significantly modified in some region of the
doping-temperature plane. The transition between superconductivity and
antiferromagnetism occurs through a phase where both order parameters coexist
with a third, dynamically generated, spin-triplet amplitude. This dynamical
generation of a new order parameter is not restricted to a system with
antiferromagnetism and d-wave superconductivity, but is a generic feature for
fermionic systems. The dynamically generated spin-triplet order parameter is
found to be robust to variations in the mean-field Hamiltonian.
