New Critical Matrix Models and Generalized Universality

TL;DR

This paper introduces a new class of multicritical matrix models with nonpolynomial actions, exploring their critical behavior, universality classes, and potential applications to QCD phase transitions.

Contribution

It develops a framework for multicritical matrix models with arbitrary eigenvalue vanishing powers and analyzes their universality properties at criticality and edges.

Findings

Eigenvalue density vanishes as arbitrary power at the origin.

Microscopic correlation functions remain in Bessel universality class off-criticality.

Critical exponents at the spectrum edge match polynomial matrix models.

Abstract

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