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

We present results of a large-scale simulation for the flavor non-singlet light hadron spectrum in quenched lattice QCD with the Wilson quark action. Hadron masses are calculated at four values of lattice spacing in the range a ≈ 0.1 -0.05 fm on lattices with a physical extent of 3 fm at five quark masses corresponding to m π /m ρ ≈ 0.75 -0.4. The calculated spectrum in the continuum limit shows a systematic deviation from experiment, though the magnitude of deviation is contained within 11%. Results for decay constants and light quark masses are also reported.

We investigate the performance of the hybrid Monte Carlo algorithm, the standard algorithm used for lattice QCD simulations involving fermions, in updating non-trivial global topological structures. We find that the hybrid Monte Carlo algorithm has serious problems decorrelating the global topological charge. This represents a warning which must be seriously considered when simulating full QCD by hybrid Monte Carlo.

We study the critical behaviour of the chira! phase transition of SU(3) lattice QCD with one species of staggered fermions in the strong coupling limit. We find a second-order phase transition which seems to be controlled by an effective action which is in the same universality class as three-dimensional 0(2) spin models. In particular, we find for the exponent b, 0.18 < 1/~<0.25, in good agreement with the three-dimensional 0(2) value, 1/b 0.21.