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.

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Results of our autocorrelation measurement performed on Fujitsu AP1000 are reported. We analyze (i) typical autocorrelation time, (ii) optimal mixing ratio between overrelaxation and pseudo-heatbath and (iii) critical behavior of autocorrelation time around cross-over region with high statistic in wide range of β for pure SU(3) lattice gauge theory on 8 4 , 16 4 and 32 4 lattices. For the mixing ratio K, small value (3-7) looks optimal in the confined region, and reduces the integrated autocorrelation time by a factor 2-4 compared to the pseudo-heatbath. On the other hand in the deconfined phase, correlation times are short, and overrelaxation does not seem to matter For a fixed value of K(=9 in this paper), the dynamical exponent of overrelaxation is consistent with 2 Autocorrelation measurement of the topological charge on 32 3 × 64 lattice at β = 6.0 is also briefly mentioned.

We measure the sweep-to-sweep autocorrelations of blocked loops below and above the deconfinement transition for SU(3) on a 16 4 lattice using 20000-140000 Monte-Carlo updating sweeps. A divergence of the autocorrelation time toward the critical β is seen at high blocking levels. The peak is near β = 6.33 where we observe 440 ± 210 for the autocorrelation time of 1 × 1 Wilson loop on 2 4 blocked lattice. The mixing of 7 Brown-Woch overrelaxation steps followed by one pseudo-heat-bath step appears optimal to reduce the autocorrelation time below the critical β. Above the critical β, however, no clear difference between these two algorithms can be seen and the system decorrelates rather fast.

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