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A three-dimensional effective theory of Polyakov loops has recently beenderived from Wilson's Yang-Mills lattice action by means of a strong couplingexpansion. It is valid in the confined phase up to the deconfinement phasetransition, for which it predicts the correct order and gives quantitativeestimates for the critical coupling. In this work we study its predictive powerfor further observables like correlation functions and the equation of state.We find that the effective theory correctly reproduces qualitative features andsymmetries of the full theory as the continuum is approached. Regardingquantitative predictions, we identify two classes of observables by numericalcomparison as well as analytic calculations: correlation functions and theirassociated mass scales cannot be described accurately from a truncatedeffective theory, due to its inherently non-local nature involving long-rangecouplings. On the other hand, phase transitions and bulk thermodynamicquantities are accurately reproduced by the leading local part of the effectivetheory. In particular, the effective theory description is numerically superiorwhen computing the equation of state at low temperatures or the properties ofthe phase transition.

Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature