  We consider a random matrix model which describes the competition between
chiral symmetry breaking and the formation of quark Cooper pairs in QCD at
finite density. We study the evolution of the phase structure in temperature
and chemical potential with variations of the strength of the interaction in
the quark-quark channel and demonstrate that the phase diagram can realize a
total of six different topologies. A vector interaction representing
single-gluon exchange reproduces a topology commonly encountered in previous
QCD models, in which a low-density chiral broken phase is separated from a
high-density diquark phase by a first-order line. The other five topologies
either do not possess a diquark phase or display a new phase and new critical
points. Since these five cases require large variations of the coupling
constants away from the values expected for a vector interaction, we conclude
that the phase diagram of finite density QCD has the topology suggested by
single-gluon exchange and that this topology is robust.
