The chiral phase transition from the exact RG
  A brief introduction is given to the concept of the effective average action. Its dependence on the averaging or coarse graining scale is governed by an exact RG equation for which nonperturbative approximation schemes are described. This formalism is applied to the computation of the equation of state for two flavor QCD within an effective linear quark meson model. Our results allow to derive the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. A precision estimate of the universal critical equation of state for the three--dimensional O(4) Heisenberg model is given. The exact RG formalism applied to the linear quark meson model is demonstrated to provide an explicit link between the O(4) universal behavior near the critical temperature and zero quark mass on one hand and the physics at low temperatures and realistic current quark masses, i.e., the domain of validity of chiral perturbation theory on the other hand. 
D.-U. Jungnickel (University of Heidelberg)