A random matrix model for chiral symmetry breaking

Abstract

We formulate a random matrix model which mimics the chiral phase transition in QCD with two light flavors. Two critical exponents are calculated. We obtain the mean field values $\beta = \frac 12 $ and $\delta = 3$. We also find that the chiral phase transition can be characterized by the dynamics of the smallest eigenvalue of the Dirac operator. This suggests an alternative order parameter which may be of relevance for lattice QCD simulations.