  We study effective Polyakov loop models for SU(N) Yang-Mills theories at
finite temperature. In particular effective models for SU(3) YM with an
additional adjoint Polyakov loop potential are considered. The rich phase
structure including a center and anti-center directed phase is reproduced with
an effective model utilizing the inverse Monte-Carlo method. The demon method
as a possibility to obtain the effective models' couplings is compared to the
method of Schwinger-Dyson equations. Thermalization effects of microcanonical
and canonical demon method are analyzed. Finally the elaborate canonical demon
method is applied to the finite temperature SU(4) YM phase transition.
