  We compare different Polyakov loop actions yielding effective descriptions of
finite-temperature SU(2) Yang-Mills theory on the lattice. The actions are
motivated by a simultaneous strong-coupling and character expansion obeying
center symmetry and include both Ising and Ginzburg-Landau type models. To keep
things simple we limit ourselves to nearest-neighbor interactions. Some
truncations involving the most relevant characters are studied within a novel
mean-field approximation. Using inverse Monte-Carlo techniques based on exact
geometrical Schwinger-Dyson equations we determine the effective couplings of
the Polyakov loop actions. Monte-Carlo simulations of these actions reveal that
the mean-field analysis is a fairly good guide to the physics involved. Our
Polyakov loop actions reproduce standard Yang-Mills observables well up to
limitations due to the nearest-neighbor approximation.
