On matrix model partition functions for QCD with chemical potential

Abstract

Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is found between the two models. This supports the universality of such fermionic partition functions, that is of products of characteristic polynomials in the complex plane. In the strong nonhermiticity limit agreement is found for an equal number of quark and conjugate flavours. For a general flavor content the equality of partition functions holds only for small chemical potential. The chiral phase transition is analyzed for an arbitrary number of quarks, where the free energy presents a discontinuity of first order at a critical chemical potential. In the case of nondegenerate flavors there is first order phase transition for each separate mass scale.

33 pages, 2 figures

References in corpus (17)

• Random Matrices close to Hermitian or unitary: overview of methods and results
• Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
• Characteristic Polynomials of Complex Random Matrix Models
• The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• Replica Limit of the Toda Lattice Equation
• Replica field theories, Painleve transcendents, and exact correlation functions
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• Universality for eigenvalue correlations at the origin of the spectrum
• On the supersymmetric partition function in QCD-inspired random matrix models
• Distributions of Dirac Operator Eigenvalues
• Generalizations of some integrals over the unitary group
• QCD Dirac operator at nonzero chemical potential: lattice data and matrix model
• 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
• Equivalence of Matrix Models for Complex QCD Dirac Spectra
• Comparing matrix models and QCD lattice data with chemical potential

Cited by in corpus (18)

• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Generation of Matrix Models by W-operators
• BGWM as Second Constituent of Complex Matrix Model
• The QCD Sign Problem for Small Chemical Potential
• The Complex Laguerre Symplectic Ensemble of Non-Hermitian Matrices
• Matrix Models and QCD with Chemical Potential
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Massive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Ratios of characteristic polynomials in complex matrix models
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Random Matrices in 2D, Laplacian Growth and Operator Theory
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Finite size scaling of meson propagators with isospin chemical potential
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Determining F_pi from spectral sum rules