Chiral Random Matrix Models : Thermodynamics, Phase Transitions and Universality

For one flavour, we observe that standard chiral random matrix models are schematic variants of the Nambu-Jona-Lasinio (NJL) models whether in vacuum or matter. The ensuing thermodynamics is that of constituent quarks, with mean-field universality in general. For two and three flavours non-standard chiral random matrix models with $U_A(1)$ breaking are suggested. For three flavours the transition is reminiscent of the isotropic-nematic transition in liquid crystals.