Z_3 Polyakov Loop Models and Inverse Monte-Carlo Methods

We study effective Polyakov loop modelsfor SU(3) Yang-Mills theoryat 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 pointthe mean field approximation agrees very well with the numerical data. Critical exponentsassociated 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.