Random matrix model for chiral symmetry breaking and color superconductivity in QCD at finite density - art. no. 094010

We consider a random matrix model which describes the competition between c hiral symmetry breaking and the formation of quark Cooper pairs in QCD at f inite 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 reali ze a total of six different topologies. A vector interaction representing s ingle-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 topologie s either do not possess a diquark phase or display a new phase and new crit ical points. Since these five cases require large variations of the couplin g constants away from the values expected for a vector interaction, we conc lude that the phase diagram of finite density QCD has the topology suggeste d by single-gluon exchange and that this topology is robust.