Toward an analytic determination of the deconfinement temperature in SU(2) LGT

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings \beta_t and \beta_s for timelike and spacelike plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders in \beta_t and to the first non-trivial order in \beta_s. The critical coupling for the deconfinement transition is determined in the (3+1) dimensional case, by the mean field method, for different values of the lattice size N_t in the compactified time direction and of the asymmetry parameter \rho = \sqrt{\beta_t/\beta_s}. We find good agreement with Montecarlo simulations in the range 1\leq N_t \leq 5, and good qualitative agreement in the same range with the logarithmic scaling law of QCD. Moreover the dependence of the results from the parameter \rho is in excellent agreement with previous theoretical predictions