Dirac spectrum, axial anomaly and the QCD chiral phase transition

The QCD phase transition is studied on 16(3) and 32(3) x 4 lattices both with and without quark loops. We introduce a new zero-flavor or quenched species of quark zeta and study the resulting chiral condensate, (<(zeta)over bar zeta>) as a function of the zeta mass, m(zeta). By examining (<(zeta)over bar zeta>) for 10(-10) less than or equal to m(zeta) less than or equal to 10 we gain considerable information about the spectrum of Dirac eigenvalues. A comparison of ma = 0.01 and 0.025 shows little dependence of the Dirac spectrum on such a light, dynamical quark mass, after an overall shift in beta is removed. The presence of sufficient small eigenvalues to support anomalous chiral symmetry breaking in the high temperature phase is examined quantitatively In an effort to enhance these small eigenvalues, (<(zeta)over bar zeta>) is also examined in the pure gauge theory in the region of the deconfinement transition with unexpected results. Above the critical temperature, the three Z(3) phases show dramatically different chiral behavior. Surprisingly, the real phase shows chiral symmetry, suggesting that a system with one flavor of staggered fermion at N-t = 4 will possess a chiral a phase transition-behavior not expected in the continuum limit.