Toward an analytic determination of the deconfinement temperature in SU(2) lattice gauge theory Original Research Article

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings βt and βs for time-like and space-like 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 non-trivial 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 a remarkable improvement in the results compared to the zeroth-order approximation in βs, leading to a reasonably good numerical agreement with the Monte Carlo simulations in the range 1 ⩽Nt5. Moreover the dependence of the results on the parameter ϱ is in excellent agreement with previous theoretical predictions.