Improved Landau gauge fixing and the suppression of finite-volume effects of the lattice gluon propagator

For the gluon propagator of pure $SU(2)$ lattice gauge theory in the Landau gauge we investigate the effect of Gribov copies and finite-volume effects. Concerning gauge fixing, we enlarge the accessible gauge orbits by adding nonperiodic $\mathbb{Z}(2)$ gauge transformations and systematically employ the simulated annealing algorithm. Strategies to keep all $\mathbb{Z}(2)$ sectors under control within reasonable CPU time are discussed. We demonstrate that the finite-volume effects in the infrared regime become ameliorated. Reaching a physical volume of about $(6.5\mathrm{fm}{)}^4$, we find that the propagator, calculated with the indicated improvements, becomes flat in the region of smallest momenta. There are first signs in four dimensions of a decrease towards vanishing momentum.

Figure 1

The lattice gluon propagator versus momentum for $\beta =2.20$ and various lattice sizes obtained by OR in comparison with FSA results for ${32}^4$.

Figure 2

The gluon propagator obtained with FSA gauge fixing in the infrared region for various lattice sizes, all simulated at $\beta =2.20$.

Figure 3

Lattice gluon propagator for zero momentum $D(0)$ obtained with the FSA method as a function of the inverse lattice size.

Figure 4

The relative difference between the propagator values obtained from fc-SA (with one copy in one random flip sector) and obtained from bc-FSA as a function of the momentum $p$ for various lattice sizes.