Chiral random matrix models: thermodynamics, phase transitions and universality

We observe that standard chiral random matrix models (ChRMM) follow from the constant mode sector 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 flavors new ChRMM with UA(1) breaking are suggested. For three flavors a first order transition is noted. The relevance of some of the results to lattice simulations in matter is discussed.