Two flavor chiral phase transition from nonperturbative flow equations

We employ nonperturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities such as the chiral condensate or the pion mass. A precision estimate of the universal critical equation of state for the three-dimensional $O\left(4\right)\mathrm{}$ Heisenberg model is presented. We explicitly connect the $O\left(4\right)\mathrm{}$ universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near $T_c$ turns out to be smaller than its zero temperature value.