Chiral Random Matrix Models : Thermodynamics, Phase Transitions and Universality

Abstract

For one flavour, we observe that standard chiral random matrix models are schematic variants of the Nambu-Jona-Lasinio (NJL) models whether in vacuum or matter. The ensuing thermodynamics is that of constituent quarks, with mean-field universality in general. For two and three flavours non-standard chiral random matrix models with $U_A(1)$ breaking are suggested. For three flavours the transition is reminiscent of the isotropic-nematic transition in liquid crystals.

One figure added. Discussion in section 4 changed. Section 5, slightly reformatted

References in corpus (12)

• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Random matrix model of QCD at finite density and the nature of the quenched limit
• Susceptibilities, the Specific Heat and a Cumulant in Two-Flavour QCD
• Baryonic Correlation Functions in the Random Instanton Vacuum
• A random matrix model for chiral symmetry breaking
• Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator
• The chiral phase transition in a random matrix model with molecular correlations
• Quenched QCD at finite density
• Phase Transitions at Finite Temperature and Dimensional Reduction for Fermions and Bosons
• The Instanton Density at Finite Temperatures
• Chiral Susceptibilities in noncompact QED: a new determination of the $\gamma$ exponent and the critical couplings

Cited by in corpus (16)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Nonhermitean Random Matrix Models
• Universal spectral correlations of the Dirac operator at finite temperature
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble
• Instantons and the Chiral Phase Transition at non-zero Baryon Density
• Critical Scaling at Zero Virtuality in QCD
• New Multicritical Random Matrix Ensembles
• Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry
• The U(1) Problem in Chiral Random Matrix Models
• A PNJL model in 0+1 Dimensions
• A Four-Fermi Model in 0+1 Dimensions in Matter
• UA(1) breaking and phase transition in chiral random matrix model
• Quaternionic R transform and non-hermitian random matrices
• Random matrix model at nonzero chemical potentials with anomaly effects
• A chiral random matrix model with 2+1 flavors at finite temperature and density