ar X iv : h ep - l at / 9 60 80 47 v 1 9 A ug 1 99 6 1 BI - TP 96 / 34 August 1996

The thermodynamics of the SU(3) gauge theory has been analyzed with tree level and tadpole improved Symanzik actions. A comparison with the continuum extrapolated results for the standard Wilson action shows that improved actions lead to a drastic reduction of finite cutoff effects already on lattices with temporal extent Nτ = 4. Results for the pressure, the critical temperature, surface tension and latent heat are presented. First results for the thermodynamics of four-flavour QCD with an improved staggered action are also presented. They indicate similarly large improvement factors for bulk thermodynamics. 1. Why improved actions are expected to improve the QCD thermodynamics Although the plasma phase of QCD does in many respects show strong non-perturbative properties (screening masses, poor convergence of perturbation theory,...), bulk thermodynamic observables like energy density and pressure do approach the non-interacting ideal gas limit at high temperatures (T) where they are expected to receive large contributions from high momentum modes, avg.momentum ∼ T. In lattice calculations T is determined through the temporal extent N τ of the lattice and the cutoff a −1 , i.e. T ≡ 1/N τ a. In the ideal gas limit the relevant momenta are therefore of the order of the cutoff , where lattice and continuum dispersion relations differ strongly from each other. Indeed this is the origin of the well-known discrepancy between the energy density of an ideal gas calculated on a finite lattice (ǫ(N τ)) and in the continuum (ǫ SB),