Toward an analytic determination of the deconfinement temperature in SU(2) L.G.T

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings βt and βs 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 βt and to the first nontrivial order in βs. 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 Nt in the compactified time direction and of the asymmetry parameter ρ = √ βt/βs. We find good agreement with Montecarlo simulations in the range 1 ≤ Nt ≤ 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 ρ is in excellent agreement with previous theoretical predictions. [email protected] [email protected]