Lattice SU(3) thermodynamics and the onset of perturbative behaviour

We present the equation of state (pressure, trace anomaly, energy density and entropy density) of the SU(3) gauge theory from lattice field theory in an unprecedented precision and temperature range. We control both finite size and cut-off effects. The studied temperature window (0.7 ... 1000T_c) stretches from the glueball dominated system into the perturbative regime, which allows us to discuss the range of validity of these approaches. From the critical couplings on fine lattices we get T_c/Λ_MS = 1.26(7) and use this ratio to express the perturbative free energy in T_c units. We also determine the preferred renormalization scale of the Hard Thermal Loop scheme and we fit the unknown g⁶ order perturbative coefficient at extreme high temperatures T > 100T_c. We furthermore quantify the nonperturbative contribution to the trace anomaly using two simple functional forms.