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

We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctuations of the Polyakov loop, as well as that of its absolute value, are considered. We analyze their properties in relation to the confinement-deconfinement phase transition. We also present results based on simulations of (2 + 1)-flavor QCD on 32(3) x 8 lattice using highly improved staggered quark action by the HotQCD collaboration. The influences of fermions on the Polyakov loop fluctuations are discussed. We show that ratios of different susceptibilities of the Polyakov loop are sensitive probes for critical behavior. We formulate an effective model for the Polyakov loop potential and constrain its parameters from existing quenched lattice data including fluctuations. We emphasize the role of fluctuations to fully explore the thermodynamics of pure gauge theory within an effective approach.