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The scaling behavior of pure gauge SU(3) in the region β = 5.85−7.60 is examined by a Monte Carlo Renormalization Group analysis. The coupling shifts induced by factor 2 blocking are measured both on 32 4 and 16 4 lattices with high statistics. A systematic deviation from naive 2-loop scaling is clearly seen. The mean field and effective coupling constant schemes explain part, but not all of the deviation. It can be accounted for by a suitable change of coupling constant, including a correction term O(g 7 ) in the 2-loop lattice β-function. Based on this improvement,M S is estimated to be 2.2(±0.1) from the analysis of the string tension σ.

We analyze temporal and spatial meson correlators in quenched lattice QCD at T ≥ 0. Below T c we observe little change in the meson properties as compared with T = 0. Above T c we observe new features: chiral symmetry restoration and signals of plasma formation, but also indication of persisting "mesonic" (metastable) states and different temporal and spatial "masses" in the mesonic channels. This suggests a complex picture of QGP in the region 1 − 1.5 T c .

We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings β 11 and β 12 corresponding to 1 × 1 and 1 × 2 loops respectively. Extensive numerical calculations of the RG flow are made in the fourth quadrant of this coupling space, i.e., β 11 > 0 and β 12 < 0. Swendsen's factor two blocking and the Schwinger-Dyson method are used to find an effective action for the blocked gauge field. The resulting renormalization group flow runs quickly towards an attractive stream which has an approximate line shape. This is numerical evidence of a renormalized trajectory which locates close to the two coupling space. A model flow equation which incorporates a marginal coupling (asymptotic scaling term), an irrelevant coupling and a non-perturbative attraction towards the strong coupling limit reproduces qualitatively the observed features. We further examine the scaling properties of an action which is closer to the attractive stream than the currently used improved actions. It is found that this action shows excellent restoration of rotational symmetry even for coarse lattices with a ∼ 0.3 fm.

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