Microscopic universality and the chiral phase transition in two flavor QCD

We reanalyze data from available finite-temperature QCD simulations near the chiral transition, with the help of chiral random matrix theory (chiral RMT). The statistical properties of the lowest-lying eigenvalues of the staggered Dirac operator for SU(3) lattice gauge theory with dynamical fermions are examined. We consider temperatures below, near, and above the critical temperature $T_c$ for the chiral phase transition. Below and above $T_c$ the statistics are in agreement with the exact analytical predictions in the microscopic scaling regime. Above $T_c$ we observe a gap in the spectral density and a distribution compatible with the Airy distribution. Near $T_c$ the eigenvalue correlations appear inconsistent with chiral RMT.