Lattice simulations for the running coupling constant of QCD

The strong coupling constant alpha_s(mu_0), taken at a fixed reference scale mu_0, is the single free parameter of QCD and should be known to the highest available precision. The value of alpha_s should also be determined with good accuracy over as large a range of scales as possible, in order to reveal potential anomalous running in the strength of the strong interaction. Lattice QCD is now able to calculate alpha_s with accuracy comparable to or better than experiment. We review the status of such lattice calculations in quenched and full QCD.Comment: 10 pages; invited seminar presented at the VIII International Workshop on Hadron Physics 2002, Bento Goncalves RS, Brazil, April 14-19, 200

Lattice Results in Coulomb Gauge

We discuss recent numerical results obtained for gluon and ghost propagators in lattice Coulomb gauge and the status of the so-called Gribov-Zwanziger confinement scenario in this gauge. Particular emphasis will be given to the eigenvalue spectrum of the Faddeev-Popov matrix.Comment: 7 pages; plenary talk presented at the QCHS7, Ponta Delgada Acores - Portugal (September 2006

How to extract information from Green's functions in Landau gauge

The infrared behavior of gluon and ghost propagators offers a crucial test of confinement scenarios in Yang-Mills theories. A nonperturbative study of these propagators from first principles is possible in lattice simulations, but one must consider significantly large lattice sizes in order to approach the infrared limit. We propose constraints based on general properties of the propagators to gain control over the extrapolation of data to the infinite-volume limit. These bounds also provide a way to relate the propagators to simpler, more intuitive quantities. We apply our analysis to the case of pure SU(2) gauge theory in Landau gauge, using the largest lattice sizes to date. Our results seem to contradict commonly accepted confinement scenarios. We argue that it is not so.Comment: 6 pages, proceedings of SPMTP08 (Dubna, June 2008), talk presented by A. Cucchier

Numerical Simulation of N-vector Spin Models in a Magnetic Field

Three-dimensional N-vector spin models may define universality classes for such diverse phenomena as i) the superfluid transition in liquid helium (currently investigated in the micro-gravity environment of the Space Shuttle) and ii) the transition from hadronic matter to a quark-gluon plasma, studied in heavy-ion collisions at the laboratories of Brookhaven and CERN. The models have been extensively studied both by field-theoretical and by statistical mechanical methods, including Monte Carlo simulations using cluster algorithms. These algorithms are applicable also in the presence of a magnetic field. Key quantities for the description of the transitions above -- such as universal critical amplitude ratios and the location of the so-called pseudo-critical line -- can be obtained from the models' magnetic equation of state, which relates magnetization, external magnetic field and temperature. Here we present an improved parametrization for the equation of state of the models, allowing a better fit to the numerical data. Our proposed form is inspired by perturbation theory, with coefficients determined nonperturbatively from fits to the data.Comment: 6 pages, 2 figures. Work presented at the IV Brazilian Meeting on Simulational Physics -- Ouro Preto - MG/Brazil, August 200