Analytic Results in (2+1)-Dimensional Finite Temperature LGT

In a (2 + 1)-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as β_c(n_t) = J_cn_t + a₁, where n_t is the number of links in the "timelike" direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the spacelike plaquettes, and we are able to compute analytically in this context the coefficient a₁ for any SU(N) gauge group; the value of J_c is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the (2 + 1)-dimensional theory, spacelike plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.