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

TL;DR

This study investigates autocorrelation times in SU(3) lattice gauge theory near the deconfinement transition, demonstrating that overrelaxed algorithms effectively reduce autocorrelation times and improve simulation efficiency.

Contribution

It provides empirical measurements of autocorrelation times in SU(3) lattice gauge theory and shows the effectiveness of overrelaxed algorithms in reducing autocorrelation near critical points.

Findings

Autocorrelation time diverges near critical $eta$ value.

Overrelaxed algorithms reduce autocorrelation times below critical $eta$.

System decorrelates quickly above the critical $eta$.

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 $\beta$ is seen at high blocking levels. The peak is near $\beta$ = 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 $\beta$. Above the critical $\beta$, however, no clear difference between these two algorithms can be seen and the system decorrelates rather fast.