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We derive three-dimensional, Z(N)-symmetric effective actions in terms ofPolyakov loops by means of strong coupling expansions, starting from thermalSU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action inthe literature, corresponding to the (spatial) strong coupling limit, is thusextended by several higher orders, as well as by additional interaction terms.We provide analytic mappings between the couplings of the effective theory andthe parameters $N_\tau,\beta$ of the original thermal lattice theory, which canbe systematically improved. We then investigate the deconfinement transitionfor the cases SU(2) and SU(3) by means of Monte Carlo simulations of theeffective theory. Our effective models correctly reproduce second order 3dIsing and first order phase transitions, respectively. Furthermore, wecalculate the critical couplings $\beta_c(N_\tau)$ and find agreement withresults from simulations of the 4d theory at the few percent level for$N_\tau=4-16$.

Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series