Systematic study of autocorrelation time in pure SU(3) lattice gauge theory

TL;DR

This study systematically investigates autocorrelation times in pure SU(3) lattice gauge theory, analyzing optimal update ratios and critical behavior across different lattice sizes and phases to improve simulation efficiency.

Contribution

It provides the first comprehensive analysis of autocorrelation times, optimal mixing ratios, and critical behavior in pure SU(3) lattice gauge theory across various lattice sizes and phases.

Findings

Optimal mixing ratio K (3-7) reduces autocorrelation time by 2-4 times in the confined phase.

Autocorrelation times are short in the deconfined phase, with overrelaxation having minimal effect.

Dynamical exponent of overrelaxation is consistent with 2 at fixed K.

Abstract

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 $\beta$ 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 $32^3 \times 64$ lattice at $\beta$ = 6.0 is also briefly mentioned.