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 thermod ynamics at work in a variety of models with spontaneously broken chira l symmetry but without confinement. This version of the model is mappe d onto chiral random matrix models, with some emphasis on the bulk beh avior of the corresponding Dirac spectrum. Phase changes in the simpli fied model show up in the form of a rearrangement in the Dirac spectru m, with edge singularities that follow from mean-field exponents. The results are shared by a variety of models, and seem to be in quantitat ive agreement with some QCD lattice simulations. We comment on the rel evance of microscopic and macroscopic universality in random matrix mo dels, and the possible motivation for these models from QCD.