Degrees of freedom and the phase transitions of two-flavor QCD

We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the linear sigma model extended by including a Polyakov loop potential, which is fitted to reproduce the pure gauge theory thermodynamics, and a coupling between the chiral fields and the Polyakov loop. Thus the resulting models have as relevant degrees of freedom the Polyakov loop and chiral fields. By comparing the extended models with the bare chiral models we can conclude that the addition of the Polyakov loop is necessary in order to obtain both qualitative and quantitative agreement with known results at finite temperatures. These results are extended to finite net-quark densities, several thermodynamical quantities are investigated in detail, and possible applications and consequences for relativistic heavy ion collision phenomenology are discussed.