Autocorrelation in Updating Pure SU(3) Lattice Gauge Theory by the use of Overrelaxed Algorithms

Abstract

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 ${\hat{I}}^2$ is seen at high blocking levels. The peak is near ${\hat{I}}^2$ = 6.33 where we observe 440 $\pm$ 210 for the autocorrelation time of $1\times 1$ 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 ${\hat{I}}^2$. Above the critical ${\hat{I}}^2$, however, no clear difference between these two algorithms can be seen and the system decorrelates rather fast.

4 pages of A4 format including 6-figures