Phase structure of Z(3)-Polyakov-loop models

We study effective lattice actions describing the Polyakov-loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of Z(3)-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean-field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches concerning the phase structure of the theories. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic, and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents nu and gamma at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state Potts model.