Thermodynamics of QCD-inspired theories

In this thesis I investigate the thermodynamics of the O(N) nonlinear sigma model and the CP^(N-1) model in 1 + 1 dimensions, which are toy models for QCD. In particular I put emphasis on the calculation of the effective potential and the pressure to next-to-leading order in 1/N. One interesting result is that the effective potential contains temperature-dependent ultraviolet divergences that vanish in the minimum. Furthermore I discuss two low-energy effective theories, the O(N) linear sigma model in 3 + 1 dimensions and the NJL model. In the O(N) model I calculate the effective potential and the pressure up to next-to-leading order in 1/N. I also discuss a rather low bound on the mass of the sigma meson in that model. The NJL model is used to calculate phase diagrams with pseudoscalar condensation and color superconductivity as a function of different quark chemical potentials. I find that phases with pseudoscalar condensation are separated from the color superconducting phases by a first order transtion.