A random matrix study of the QCD phase diagram

In this talk, I will consider random matrix models which describe the thermodynamic competition between diquark and chiral condensation. I will first study the evolution of the phase structure as a function of temperature, quark chemical potential, number of colors, and coupling constants. I will demonstrate that there is only a finite set of topologies allowed for the phase diagram and that the topology associated with QCD interactions is robust against moderate variations of the coupling constants. Next, I will discuss various schemes for treating the quark temperature and examine their effects on the phase diagram and on bulk thermodynamic properties. Finally, I will examine the properties of the spectral correlators and verify that the introduction of color and spin degrees of freedom does not alter those properties which ought to be protected by chiral symmetry/