New Critical Matrix Models and Generalized Universality

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.

LaTeX, 25 pages, 1 figure; references added, NPB to appear

References in corpus (1)

• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD

Cited by in corpus (8)

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• Multicritical edge statistics for the momenta of fermions in non-harmonic traps
• Universal random matrix correlations of ratios of characteristic polynomials at the spectral edges
• Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• Divergent chiral condensate in the quenched Schwinger model
• Weak and strong confinement in the Freud random matrix ensemble and gap probabilities
• Perturbed generalized multicritical one-matrix models