The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N τ = 4, 6 and 8 and spatial extent N σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32 4 lattices to fix the temperature scale. An extrapolation to the continuum limit yields T c / √ σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≃ 5T c . For the spatial string tension we find √ σ s /T = 0.566(13)g 2 (T ) with g 2 (5T c ) ≃ 1.5.

Through a detailed investigation of the $SU(3)$ gauge theory at finite temperature on lattices of various size we can control finite lattice cut-off effects in bulk thermodynamic quantities. We calculate the pressure and energy density of the $SU(3)$ gauge theory on lattices with temporal extent $N_\tau = 4$, 6 and 8 and spatial extent $N_\sigma =16$ and 32. The results are extrapolated to the continuum limit. We find a deviation from ideal gas behaviour of (15-20)\%, depending on the quantity, even at temperatures as high as $T\sim 3T_c$. A calculation of the critical temperature on lattices with temporal extent $N_\tau = 8$ and 12 and the string tension on $32^4$ lattices at the corresponding critical couplings is performed to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrt{\sigma} = 0.629(3)$.Comment: 12 pages, LaTeX2e, 5 figures in a seperate uuencoded compressed file. fixed end{document

The pressure near the deconfinement transition as determined up to now in lattice gauge theories shows unphysical behaviour: it can become negative and may in SU (3) even have a gap at the transition. This has been attributed to the use of only perturbatively known derivatives of coupling constants. We propose a method to evaluate the pressure, which works without these derivatives, and is valid on large lattices. In SU(2) we study the finite-volume effects and show that for lattices with spatial extent N, ~> 15 these effects are negligible. In SU ( 3 ) we then obtain a positive and continuous pressure. The influence of non-perturbative corrections to the fl-function on the energy density are investigated and found to be important, in particular for the latent heat.

After reviewing the euclidean formulation of the thermodynamics for quantum spin systems, we develop the corresponding formalism for SU(N) gauge fields on the lattice The results are then evaluated for the SU(2) system, using Monte Carlo simulation on lattices of (space × temperature) size 103N 2,3,4,5 At hagh temperature, the system exhibits Stefan-Boltzmann behavlour, with three gluomc colour degrees of freedom At T~ ~ 43A~_ (215 MeV), the transiuon to "hadromc" behawour occurs, signalled by a sharp peak in the specific heat From the behawour below the deconfinement transition (T< Tc), we obtain m G ~ 200A L (1000 MeV) for the mass of the lowest gluomum state (glueball)

The lattice data for the energy density of SU (2) gauge theory are calculated with non-perturbative derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the non-perturbative beta function in accord with the measured critical temperature and ∆β−values and ii) a non-perturbative calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near T c . It is shown that at the critical temperature the energy density is scaling as a function of V T 3 with the corresponding 3d Ising model critical exponents. The value of ǫ(T c )/T 4 c in the continuum limit is estimated to be 0.256(23). In the high temperature regime the energy density is approaching its weak coupling limit from below, at T /T c ≈ 2 it has reached only about 70% of the limit.