The strong coupling expansion of the lattice gauge action leads to a Polyakov loop model that effectively describes the gluodynamic at low temperatures and together with the hopping expansion of the fermion determinant allows for insights into the QCD phase diagram at finite density and low temperatures, although the accessible pion masses are rather large. At high temperatures the strong coupling expansion breaks down and it is expected that the interaction of Polyakov loops becomes non-local. Therefore we use inverse Monte-Carlo methods to map SU(2) gluodynamic to different non-local Polyakov loop models. We take into account Polyakov loops in higher representations and gradually add interaction terms at larger distances to find out how well we can describe the full theory and to investigate the convergent behavior towards the full theory. We investigate thereby different kind of observables and are particularly interested in the quality of our models in the large volume limit. Furthermore we try to determine a possibly analytical behavior for the fall-off of the couplings of the non-local terms (with respect to the interaction distance). We test different possibilities for such a behavior, compare our results to existing statements and try to find connections to the correlation length of the full theory.
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