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

Abstract

The spectrum of low-lying eigenvalues of the 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 $T={T}_{c}$, though not going to zero. At ${T}_{c}^{\ensuremath{'}}\ensuremath{\approx}1.5{T}_{c}\ensuremath{\approx}480\text{ }\text{ }\mathrm{MeV}$ the chiral condensate decreases rapidly once again and becomes either very small or zero. At $T<{T}_{c}$ the distributions of small eigenvalues are universal and are well described by the chiral orthogonal ensemble of random matrices. In the temperature range above ${T}_{c}$ 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.