PUB - Publikationen an der Universität Bielefeld

We study a class of one-matrix models with an action containing nonpolynomialterms. By tuning the coupling constants in the action to criticality we obtainthat the eigenvalue density vanishes as an arbitrary real power at the origin,thus defining a new class of multicritical matrix models. The correspondingmicroscopic scaling law is given and possible applications to the chiral phasetransition in QCD are discussed. For generic coupling constants off-criticalitywe prove that all microscopic correlation functions at the origin of thespectrum remain in the known Bessel universality class. An arbitrary number ofDirac mass terms can be included and the corresponding massive universality ismaintained as well. We also investigate the critical behavior at the edge ofthe spectrum: there, in contrast to the behavior at the origin, we find thesame critical exponents as derived from matrix models with a polynomial action.