  We study effective Polyakov loop models for SU(3) Yang-Mills theory at finite
temperature. A comprehensive mean field analysis of the phase diagram is
carried out and compared to the results obtained from Monte-Carlo simulations.
We find a rich phase structure including ferromagnetic and antiferromagnetic
phases. Due to the presence of a tricritical point the mean field approximation
agrees very well with the numerical data. Critical exponents associated with
second-order transitions coincide with those of the Z_3 Potts model. Finally,
we employ inverse Monte-Carlo methods to determine the effective couplings in
order to match the effective models to Yang-Mills theory.

High Energy Physics - Lattice