Monte Carlo calculation for the effective couplings of Polyakov loops

We report a Monte Carlo calculation of effective coupling constants of Polyakov loops in the (2+1)-dimensional Z(2) lattice gauge theory. We exhibit the method in general as applied to (d+1)-dimensional SU(N) lattice gauge theories. The calculations were carried out on a special-purpose array processor. In addition to nearest-neighbor coupling twelve types of effective couplings are considered. At least nine of them give non-negligible contributions at the deconfinement transition point. We do not see a rapid falloff of long-range multiloop couplings and therefore cannot draw any firm conclusions concerning the conjecture of Svetitsky and Yaffe