We present SU(3) gluon propagators calculated on 48 2 48 2 48 2 N t lattices at = 6:8 where N t = 64 (corresponding the connement phase) and N t = 16 (deconnement) with the bare gauge parameter,, set to be 0.1. In order to avoid Gribov copies, we employ the stochastic gauge xing algorithm. Gluon propagators show quite dierent behavior from those of massless gauge elds:(1) In the connement phase, G(t) shows massless behavior at small and large t, while around 5 < t < 15 it behaves as massive particle, and (2) eective mass observed in G(z) becomes larger as z increases. (3) In the deconnement phase, G(z) shows also massive behavior but eective mass is less than in the connement case. In all cases, slope masses are increasing functions of t or z, which can not be understood as addtional physical poles.
Abstract:We evaluate the Λ-parameter in the MS scheme for the pure SU(3) gauge theory with the twisted gradient flow (TGF) method. A running coupling constant g 2 TGF (1/L) is defined in a finite volume box with size of L 4 with the twisted boundary condition. This defines the TGF scheme. Using the step scaling method for the TGF coupling with lattice simulations, we can evaluate the Λ-parameter non-perturbatively in the TGF scheme. In this paper we determine the dimensionless ratios, Λ TGF / √ σ and r 0 Λ TGF together with the Λ-parameter ratio Λ SF /Λ TGF on the lattices numerically. Combined with the known ratio Λ MS /Λ SF , we obtain Λ MS / √ σ = 0.5315(81)( +269 −48 ) and r 0 Λ MS = 0.6062(92)( +309 −52 ), where the first error is statistical one and the second is our estimate of systematic uncertainty.
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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