Polyakov loop fluctuations in SU(3) lattice gauge theory and an effective gluon potential

We discuss results on the Polyakov loop susceptibilities in SU(3)lattice gauge theory. The longitudinal and transverse fluctuations of thePolyakov loop, as well as, that of its absolute value will be introducedin the context of the confinement-deconfinement phase transition.We will indicate the influences of fermionson the Polyakov loop fluctuations, based on lattice calculations in 2- and(2+1)-flavors QCD. We show, that ratios of different susceptibilities ofthe Polyakov loop are excellent probes of critical behavior. We willformulate an effective model for thePolyakov loop coupled to fermions and discus its applications to QCDthermodynamics. We emphasize the role of fluctuations to fully exploreproperties of QCD in the limit of heavy flavours.