I.L. Bogolubsky

Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared

Abstract We present recent results for the Landau-gauge gluon and ghost propagators in SU ( 3 ) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L = 64 to L = 96 at β = 5.70 , thus reaching “deep infrared” momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a simulated annealing technique which allows us to reach gauge-functional values closer to the global maxima than standard approaches do. Our results are consistent with the so-called decoupling solutions found for Dyson–Schwinger and functional renormalization group equations.

The Landau gauge gluon and ghost propagators in 4D SU(3) gluodynamics in large lattice volumes

I. L. Bogolubsky a, E.-M. Ilgenfritzb, M. Muller-Preusskerb, and A. Sternbeckc a Joint Institute for Nuclear Research, 141980 Dubna, Russia b Humboldt Universitat zu Berlin, Institut fur Physik, 12489 Berlin, Germany c CSSM, School of Chemistry & Physics, University of Adelaide, SA 5005, Australia E-mail: bogolubs@lxpub04.jinr.ru, ilgenfri@physik.hu-berlin.de, mmp@physik.hu-berlin.de, andre.sternbeck@adelaide.edu.au

Landau gauge gluon and ghost propagators from lattice QCD

We report on recent numerical computations of the Landau gauge gluon and ghost propagators as well as of the ghost-gluon-vertex function in pure SU(3) Yang-Mills theory and in full QCD on the lattice. Special emphasis is paid to the low momentum region. In particular, we present new data for the gluon propagator at momenta below 300 MeV. We also discuss different systematic effects as there are finite-size, lattice discretization and Gribov copy but also unquenching effects. A MOM-scheme running coupling as(q2) based on the ghost-gluon vertex is calculated and found to decrease for momenta below 550 MeV, even though the renormalization constant of the vertex deviates only weakly from being constant.

Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets all gauge (i.e. Gribov) copies originate mainly from the zero-momentum modes of the gauge fields. The removal of the zero–momentum modes turns out to be necessary for reaching the absolute maximum of the gauge functional F(θ) . A new gauge fixing procedure – zero-momentum Lorentz gauge – is proposed.

Polyakov loops and binder cumulants in SU(2) theory on large lattices

Abstract Polyakov loops and their Binder cumulants are computed on large asymmetric lattices N 4 × N s 3 with N s ⪢ N 4 in order to determine the critical couplings β c = (4/ g 2 ) crit at the finite temperature phase transition for SU (2) lattice gauge theory. Preliminary results for lattices with time extent N 4 = 8, 12 and 16 are presented.

Fermionic correlators and zero-momentum modes in quenched lattice QED

Abstract For the Lorentz gauge the influence of various Gribov gauge copies on the fermion propagator is investigated in quenched compact lattice QED. Within the Coulomb phase besides double Dirac sheets the zero-momentum modes of the gauge fields are shown to cause the propagator to deviate strongly from the perturbatively expected behaviour. The standard way to extract the fermion mass fails. The recently proposed zero-momentum Lorentz gauge is demonstrated to cure the problem.

2D topological solitons in the gauged easy-axis Heisenberg antiferromagnet model

Abstract Field equations of the 3-component U(1) gauged sigma model (“the A3M model”) with spontaneously broken Z (2) symmetry are presented for ( D + 1)-dimensional space-time. Localized solutions of the two-dimensional A3M model with the unit topological charge are found numerically; these topological solitons describe (at least for small values of a parameter p , p p 0 ) stable bound states of the unit 3-component “easy-axis” Heisenberg field and the Maxwell field. Possible physical implications of 2D and 3D topological solitons of the A3M model are discussed.

Gribov copies and gauge variant correlators in U(1) lattice gauge theory

We discuss the influence of Dirac sheets and zero–momentum modes on the gauge variant photon correlators ( τ; ~ p) with ~

Lattice results on gluon and ghost propagators in landau gauge

We present clear evidence of strong effects of Gribov copies in Landau gauge gluon and ghost propagators computed on the lattice at small momenta by employing a new approach to Landau gauge fixing and a more effective numerical algorithm. It is further shown that the new approach substantially decreases notorious finite-volume effects.

Performance studies of the two-step multiboson algorithm in compact lattice QED

Abstract The performance of the two-step multiboson (TSMB) algorithm is investigated in comparison with the hybrid Monte Carlo (HMC) method for compact lattice QED with standard Wilson fermions both in the Coulomb and confinement phases. The restriction to QED allows for extensive measurements of autocorrelation times. Preliminary results show that the TSMB algorithm is at least competitive with standard HMC.