  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.
