For SU (2) lattice gauge theory we study numerically the infrared behavior of the Landau gauge ghost and gluon propagators with the special accent on the Gribov copy dependence. Applying a very efficient gauge fixing procedure and generating up to 80 gauge copies we find that the Gribov copy effect for both propagators is essential in the infrared. In particular, our best copy dressing function of the ghost propagator approaches a plateau in the infrared, while for the random first copy it still grows. Our best copy zero-momentum gluon propagator shows a tendency to decrease with growing lattice size which excludes singular solutions. Our results look compatible with the so-called decoupling solution with a non-singular gluon propagator. However, we do not yet consider the Gribov copy problem to be finally resolved.

The behavior of the Landau gauge gluon and ghost propagators is studied in pure SU (3) gauge theory at non-zero temperature on the lattice. We concentrate on the momentum range [0.6, 2.0] GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects at temperatures close to the deconfinement phase transition at T = Tc and within the restricted range of momenta. Since the longitudinal component DL(q) turns out to be most sensitive with respect to the phase transition we propose some combinations of DL(q) signalling the transition much like "order parameters".

We reinvestigate the problem of Gribov ambiguities within the Landau (or Lorentz) gauge for the ghost and gluon propagators in pure SU (2) lattice gauge theory. We make use of the full symmetry group of the action taking into account large, i.e. non-periodic Z(2) gauge transformations leaving lattice plaquettes invariant. Enlarging in this way the gauge orbits for any given gauge field configuration the Landau gauge can be fixed at higher local extrema of the gauge functional in comparison with standard (overrelaxation) techniques. This has a clearly visible effect not only for the ghost propagator at small momenta but also for the gluon propagator, in contrast to the common belief.

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU (2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm) 4 to (7.3 fm) 4 . Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (non-perturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator Dren(p) at momenta |p| > ∼ 0.6 GeV . The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found the Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple pole-like behavior ∼ (p 2 +m 2 g ) −1 for momenta |p| < ∼ 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width -for a physical volume (5.0 fm) 4 -we estimate a corresponding infrared (mass) scale to be mIR ∼ 0.7 GeV.

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 Z(2) gauge transformations and systematically employ the simulated annealing algorithm. Strategies to keep all 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 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.