The interplay between antiferromagnetism and d-wave superconductivity is st
udied in a mean-field approximation for a generic microscopic Hamiltonian w
ith short-range repulsion and near-neighbor attraction. In the presence of
competing microscopic interactions, the phase boundaries of antiferromagnet
ic apd 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 coexi
st with a third, dynamically generated, spin-tripler amplitude. This dynami
cal generation of a new order parameter is not restricted to a system with
antiferromagnetism and cl-wave superconductivity, but is a generic feature
for fermionic Systems. The dynamically generated spin;triplet order paramet
er is found to be robust to variations in the mean-field Hamiltonian.