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

Understand

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.