Thermodynamics of QCD low-energy models and the derivative expansion of the effective action

We study the equation of state of a strongly interacting theory of relativistic bosons and chiral fermions in the vicinity and above the chiral phase transition temperature. Our model resembles presently used low-energy models of QCD in many ways, but its simplicity allows us to study systematically various approximation schemes by means of a derivative expansion. In particular, we compare the results for the phase transition temperature, equation of state and the thermal mass of the scalar fields obtained in various approximations. We find that the large-N_c approximation, being the zeroth order of our approximation, deviates significantly from approximation schemes in which effects of (Pseudo-) Goldstone modes have been taken into account, even at high temperatures and even if we allow for a finite explicit symmetry breaking. The important role of the (Pseudo-) Goldstone modes is also manifested in the phenomenon of "local order" which is missing in large-N_c studies.