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 βc(nt) = Jcnt + a1, where nt is the number of links in the “time-like” direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the space-like plaquettes, and we are able to compute analytically in this context the coefficient a1 for any SU(N) gauge group; the value of Jc 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, space-like plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.