Scaling, asymptotic scaling and Symanzik improvement. Deconfinement temperature in SU(2) pure gauge theory

We report on a high statistics simulation of SU(2) pure gauge field theory at finite temperature, using Symanzik action. We determine the critical coupling for the deconfinement phase transition on lattices up to 8 x 24, using Finite Size Scaling techniques. We find that the pattern of asymptotic scaling violation is essentially the same as the one observed with conventional, not improved action. On the other hand, the use of effective couplings defined in terms of plaquette expectation values shows a precocious scaling, with respect to an analogous analysis of data obtained by the use of Wilson action, which we interpret as an effect of improvement