Chiral symmetry in matter

We provide a schematic view to some general aspects of chiral symmetry in matter using mean-field arguments. We use a simplified version of the Nambu-Jona-Lasinio model to formulate the ideas behind the thermodynamics at work in a variety of models with spontaneously broken chiral symmetry but without confinement. This version of the model is mapped onto chiral random matrix models, with some emphasis on the bulk behavior of the corresponding Dirac spectrum. Phase changes in the simplified model show up in the form of a rearrangement in the Dirac spectrum, with edge singularities that follow from mean-field exponents. The results are shared by a variety of models, and seem to be in quantitative agreement with some QCD lattice simulations. We comment on the relevance of microscopic and macroscopic universality in random matrix models, and the possible motivation for these models from QCD.