Deconfinement transition and the Z(N) clock model

The d-dimensional N-state (Z(N)) clock model is derived from the (d+1)-dimensional finite-temperature SU(N) lattice gauge theory with fermions, restricting temporal link variables to the center subgroup of SU(N) and employing a mean field treatment of spatial link variables. A set of explicit relations between the coupling constants of SU(N) and Z(N) theories is obtained. For the pure gauge case, one of these relations, combined with Monte Carlo simulations, gives an estimate of the deconfinement transition temperature, Tsub(c). For the case of SU(2) theory, it is found that Tsub(c) derived from this relation is in good agreement with Tsub(c) obtained by explicit calculation of the Wilson line. This supports the conjecture that the deconfinement transition in SU(N) lattice gauge theory is in the same universality class as the Z(N) clock model. Finally, we discuss the effect of fermions on the nature of the transition and point out some subleties for the case of SU(3) theory. (orig.)