V.K. Mitrjushkin

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale mIR

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){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 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 polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.

The Density of monopoles in SU(2) lattice gauge theory

Abstract We investigate the density ϱ of monopoles in SU(2) gauge theory. We find some evidence for scaling behavior, suggesting that ϱ is a physical quantity. The value ϱ = (66 Λ L ) 3 is obtained. Below a certain critical volume the monopole density rapidly decreases.

Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory

For SU(2) lattice gauge theory, we study numerically the infrared behavior of the Landau-gauge ghost and gluon propagators with a 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 continues to grow. Our best copy zero-momentum gluon propagator shows a tendency to decrease with growing lattice size, which excludes singular solutions. Our results seem compatible with the so-called decoupling solution with a nonsingular gluon propagator. However, we do not yet consider the Gribov copy problem to be resolved.

Landau gauge gluon and ghost propagators at finite temperature from quenched lattice QCD

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=T_c and within the restricted range of momenta. Since the longitudinal component D_L(q) turns out to be most sensitive with respect to the phase transition we propose some combinations of D_L(q) signalling the transition much like order parameters.

Practical problems to compute the ghost propagator inSU(2)lattice gauge theory

In SU(2) lattice pure gauge theory we study numerically the dependence of the ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau) gauge. We find that the effect of Gribov copies is essential in the scaling window region, however, it tends to decrease with increasing beta. On the other hand, we find that at larger beta-values very strong fluctuations appear which can make problematic the calculation of the ghost propagator.

Landau gauge ghost and gluon propagators in SU(2) lattice gauge theory : Gribov ambiguity reexamined

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. nonperiodic, 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.

Phase structure of the SU(2) lattice gauge Higgs theory

Abstract Phase structure of the SU(2) lattice gauge Higgs theory is investigated by the Monte Carlo method and by an approximate calculation of an effective potential. Higgs fields are considered in the fundamental representation, and the radial mode of Higgs fields is not frozen. Two different radial measures for a radially varied Higgs field are used. Phase diagrams of the theory are determined, and a strong dependence on the choice of radial measure of scalar fields is manifested.

Scaling in the positive plaquette model and universality in SU(2) lattice gauge theory

We investigate universality, scaling, the beta-function and the topological charge in the positive plaquette model for SU(2) lattice gauge theory. Comparing physical quantities, like the critical temperature, the string tension, glueball masses, and their ratios, we explore the effect of a complete suppression of a certain lattice artifact, namely the negative plaquettes, for SU(2) lattice gauge theory. Our result is that this modification does not change the continuum limit, i.e., the universality class. The positive plaquette model and the standard Wilson formulation describe the same physical situation. The approach to the continuum limit given by the beta-function in terms of the bare lattice coupling, however, is rather different: the beta-function of the positive plaquette model does not show a dip like the model with standard Wilson action.Abstract We investigate universality, scaling, the β-function and the topological charge in the positive plaquette model for SU(2) lattice gauge theory. Comparing physical quantities, like the critical temperature, the string tension, glueball masses, and their ratios, we explore the effect of a complete suppression of a certain lattice artifact, namely the negative plaquettes, for SU(2) lattice gauge theory. Our result is that this modification does not change the continuum limit, i.e., the universality class. The positive plaquette model and the standard Wilson formulation describe the same physical situation. The approach to the continuum limit given by the β-function in terms of the bare lattice coupling, however, is rather different: the β-function of the positive plaquette model does not show a “dip” like the model with standard Wilson action.

Topology across the finite temperature transition studied by overimproved cooling in gluodynamics and QCD

Gluodynamics and two-flavor QCD at non-zero temperature are studied with the so-called overimproved cooling technique under which caloron solutions may remain stable. We consider topological configurations either at the first occuring stable plateau of topological charge or at the first (anti)selfdual plateau and find the corresponding topological susceptibility at various temperatures on both sides of the thermal transition or crossover. In pure gluodynamics the topological susceptibility drops sharply at the deconfinement temperature while in full QCD it decreases smoothly at temperatures above the pseudocritical one. The results are close to those calculated by other methods. We interpret our findings in terms of the (in)stability of calorons with non-trivial holonomy and their dyon constituents against overimproved cooling.

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.