Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory

Abstract

The spectrum of low-lying eigenvalues of overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition defined by the expectation value of the Polyakov line. The value of the chiral condensate obtained from the Banks-Casher relation is found to drop down rapidly at T = Tc, though not going to zero. At Tc' = 1.5 Tc = 480 MeV the chiral condensate decreases rapidly one again and becomes either very small or zero. At T < Tc the distributions of small eigenvalues are universal and are well described by chiral orthogonal ensemble of random matrices. In the temperature range above Tc where both the chiral condensate and the expectation value of the Polyakov line are nonzero the distributions of small eigenvalues are not universal. Here the eigenvalue spectrum is better described by a phenomenological model of dilute instanton - anti-instanton gas.

8 pages RevTeX, 5 figures, 2 tables

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• Phases of SU(3) Gauge Theories with Fundamental Quarks via Dirac Spectral Density
• Chiral superfluidity of the quark-gluon plasma
• A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices
• Completing the picture for the smallest eigenvalue of real Wishart matrices
• Quark mass dependence of the vacuum electric conductivity induced by the magnetic field in SU(2) lattice gluodynamics
• Two-flavor QCD at finite temperature and chemical potential in a functional approach
• Gapless Dirac Spectrum at High Temperature
• Janossy densities for chiral random matrix ensembles and their applications to two-color QCD