arXiv subjects

Tereza Mendes

Publications and source records attributed to Tereza Mendes.

At least 73 records · Page 4Linked to original sources

arXiv2006

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.

hep-lat↗

arXiv2006

Propagators in Yang-Mills theory for different gauges

Green's functions are gauge-dependent quantities. Thus, the manifestation of confinement in these correlation functions also depends on the gauge. Here we use lattice gauge theory to study the gluon and the ghost propagators in a gauge (the so-called lambda-gauge) interpolating between the Landau and the Coulomb gauge. Results are compared to the usual minimal Landau gauge.

hep-lat↗

arXiv2006

On the infrared behavior of Green's functions in Yang-Mills theory

Non-perturbative properties of QCD, such as color confinement, are encoded in the infrared behavior of correlation functions, e.g. propagators and vertices. Various analytic predictions have been suggested for these quantities in various gauges. Here we numerically test these predictions using lattice gauge theory. In particular, we present results for the 2- and 3-point functions for SU(2) Landau-gauge Yang-Mills theory in three and in four dimensions. Special attention is paid to systematic finite-volume effects. The gluon and ghost propagators are also evaluated in the so-called interpolating gauge (between the Landau and the Coulomb gauge), in order to study their gauge-dependence. Finally, we consider these propagators in Landau gauge at finite temperature, with the aim of understanding the effect of the deconfinement phase transition on their infrared behavior. All our results are compatible with the so-called Gribov-Zwanziger confinement scenario.

hep-lat↗

arXiv2006

Lattice Results for the QCD Phase Transition

We discuss recent results for the phase transition in finite-temperature QCD from numerical (Monte Carlo) simulations of the lattice-regularized theory. Emphasis is given to the case of two degenerate light-quark flavors. The order of the transition in this case, which could have cosmological implications, has not yet been established.

hep-lat↗

arXiv2006

Propagators, Running Coupling and Condensates in Lattice QCD

We present a review of our numerical studies of the running coupling constant, gluon and ghost propagators, ghost-gluon vertex and ghost condensate for the case of pure SU(2) lattice gauge theory in the minimal Landau gauge. Emphasis is given to the infrared regime, in order to investigate the confinement mechanisms of QCD. We compare our results to other theoretical and phenomenological studies.

hep-ph↗

arXiv2006

Short-time Dynamics of Percolation Observables

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte-Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte-Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interprete percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

cond-mat.stat-mech↗

arXiv2006

Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory

Green's functions are a central element in the attempt to understand non-perturbative phenomena in Yang-Mills theory. Besides the propagators, 3-point Green's functions play a significant role, since they permit access to the running coupling constant and are an important input in functional methods. Here we present numerical results for the two non-vanishing 3-point Green's functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e. the three-gluon vertex and the ghost-gluon vertex, considering various kinematical regimes. In this exploratory investigation the lattice volumes are limited to 20^3 and 30^3 at beta=4.2 and beta=6.0. We also present results for the gluon and the ghost propagators, as well as for the eigenvalue spectrum of the Faddeev-Popov operator. Finally, we compare two different numerical methods for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source and the plane-wave-source methods.

hep-lat↗

arXiv2006

Infrared behavior of gluon and ghost propagators from asymmetric lattices

We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU(2) gauge theory. Data have been obtained using asymmetric lattices (V = 20^2 X 40, 20^2 X 60, 8^2 X 64, 8^2 X 140, 12^2 X 140 and 16^2 X 140) for the lattice coupling beta = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V. By comparing these results with data obtained using symmetric lattices (V = 60^3 and 140^3), we find that both propagators suffer from systematic effects in the infrared region (p \lesssim 650 MeV). In particular, the gluon (respec. ghost) propagator is less IR-suppressed (respec. enhanced) than in the symmetric case. We discuss possible implications of the use of asymmetric lattices.

hep-lat↗

arXiv2005

Ghost condensation on the lattice

We perform a numerical study of ghost condensation -- in the so-called Overhauser channel -- for SU(2) lattice gauge theory in minimal Landau gauge. The off-diagonal components of the momentum-space ghost propagator G^{cd}(p) are evaluated for lattice volumes V = 8^4, 12^4, 16^4, 20^4, 24^4 and for three values of the lattice coupling: β= 2.2, 2.3, 2.4. Our data show that the quantity ϕ^b(p) = ε^{bcd} G^{cd}(p) / 2 is zero within error bars, being characterized by very large statistical fluctuations. On the contrary, |ϕ^b(p)| has relatively small error bars and behaves at small momenta as L^{-2} p^{-z}, where L is the lattice side in physical units and z \approx 4. We argue that the large fluctuations for ϕ^b(p) come from spontaneous breaking of a global symmetry and are associated with ghost condensation. It may thus be necessary (in numerical simulations at finite volume) to consider |ϕ^b(p)| instead of ϕ^b(p), to avoid a null average due to tunneling between different broken vacua. Also, we show that ϕ^b(p) is proportional to the Fourier-transformed gluon field components {\widetilde A}_μ^b(q). This explains the L^{-2} dependence of |ϕ^b(p)|, as induced by the behavior of | {\widetilde A}_μ^b(q) |. We fit our data for |ϕ^b(p)| to the theoretical prediction (r / L^2 + v) / (p^4 + v^2), obtaining for the ghost condensate v an upper bound of about 0.058 GeV^2. In order to check if v is nonzero in the continuum limit, one probably needs numerical simulations at much larger physical volumes than the ones we consider. As a by-product of our analysis, we perform a careful study of the color structure of the inverse Faddeev-Popov matrix in momentum space.

hep-lat↗

arXiv2005

Positivity violation for the lattice Landau gluon propagator

We present explicit numerical evidence of reflection-positivity violation for the lattice Landau gluon propagator in three-dimensional pure SU(2) gauge theory. We use data obtained at very large lattice volumes (V = 80^3, 140^3) and for three different lattice couplings in the scaling region (beta = 4.2, 5.0, 6.0). In particular, we observe a clear oscillatory pattern in the real-space propagator C(t). We also verify that the (real-space) data show good scaling in the range t \in [0,3] fm and can be fitted using a Gribov-like form. The violation of positivity is in contradiction with a stable-particle interpretation of the associated field theory and may be viewed as a manifestation of confinement.

hep-lat↗

arXiv2004

Equation of State for Spin Systems with Goldstone Bosons: the 3d O(4) Case

We propose an improved parametric form for the equation of state of three-dimensional O(N) spin systems. The proposed form is a series expansion with two sets of terms, which contribute (mainly) separately to the description of the high- and low-temperature regions of the phase diagram. Our goal is a better description of the low-temperature phase at zero magnetic field (i.e. the coexistence line), characterized by singularities induced by Goldstone modes. We test our proposed form by comparison with existing Monte Carlo data for the N=4 case, which is of interest in studies of the QCD phase transition and for which the Goldstone-mode effects are quite pronounced. We find that the description of the numerical equation of state is indeed improved with respect to other fitting forms. In all cases considered we determine the coefficients nonperturbatively, from fits to the data. As a consequence, we are able to obtain a very precise characterization of the pseudo-critical line for the model.

hep-lat↗

arXiv2003

Propagators and running coupling from SU(2) lattice gauge theory

We perform numerical studies of the running coupling constant alpha_R(p^2) and of the gluon and ghost propagators for pure SU(2) lattice gauge theory in the minimal Landau gauge. Different definitions of the gauge fields and different gauge-fixing procedures are used respectively for gaining better control over the approach to the continuum limit and for a better understanding of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex renormalization constant is finite in the continuum limit, confirming earlier results by all-order perturbation theory. In the low momentum regime, the gluon form factor is suppressed while the ghost form factor is divergent. Correspondingly, the ghost propagator diverges faster than 1/p^2 and the gluon propagator appears to be finite. Precision data for the running coupling alpha_R(p^2) are obtained. These data are consistent with an IR fixed point given by lim_{p \to 0} alpha_R(p^2) = 5(1).

hep-lat↗

arXiv2003

Computational Aspects of Lattice QCD

Monte Carlo simulations applied to the lattice formulation of quantum chromodynamics (QCD) enable a study of the theory from first principles, in a nonperturbative way. After over two decades of developments in the methodology for this study and with present-day computers in the teraflops range, lattice-QCD simulations are now able to provide quantitative predictions with errors of a few percent. This means that these simulations will soon become the main source of theoretical results for comparison with experiments in physics of the strong interactions. It is therefore an important moment for the beginning of Brazilian participation in the field.

hep-lat↗

arXiv2003

Parallel implementation of a lattice-gauge-theory code: studying quark confinement on PC clusters

We consider the implementation of a parallel Monte Carlo code for high-performance simulations on PC clusters with MPI. We carry out tests of speedup and efficiency. The code is used for numerical simulations of pure SU(2) lattice gauge theory at very large lattice volumes, in order to study the infrared behavior of gluon and ghost propagators. This problem is directly related to the confinement of quarks and gluons in the physics of strong interactions.

hep-lat↗

arXiv2003

Critical Slowing-Down in SU(2) Landau-Gauge-Fixing Algorithms at beta = infinity

We evaluate numerically and analytically the dynamic critical exponent $z$ for five gauge-fixing algorithms in SU(2) lattice Landau-gauge theory by considering the case $β= \infty$. Numerical data are obtained in two, three and four dimensions. Results are in agreement with those obtained previously at finite $β$ in two dimensions. The theoretical analysis, valid for any dimension $d$, helps us clarify the tuning of these algorithms. We also study generalizations of the overrelaxation algorithm and of the stochastic overrelaxation algorithm and verify that we cannot have a dynamic critical exponent $z$ smaller than 1 with these local algorithms. Finally, the analytic approach is applied to the so-called $λ$-gauges, again at $β= \infty$, and verified numerically for the two-dimensional case.

hep-lat↗

arXiv2003

SU(2) Landau gluon propagator on a 140^3 lattice

We present a numerical study of the gluon propagator in lattice Landau gauge for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2, 5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V we observe a decreasing gluon propagator for momenta smaller than p_{dec} = 350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem to indicate an infra-red critical exponent kappa slightly above 0.6, in agreement with recent analytic results.

hep-lat↗

arXiv2002

Running coupling constant and propagators in SU(2) Landau gauge

We present a numerical study of the running coupling constant and of the gluon and ghost propagators in minimal Landau gauge. Simulations are done in pure SU(2) lattice gauge theory for several values of beta and lattice sizes. We use two different lattice setups.

hep-lat↗

arXiv2001

Finite-size scaling for two-flavor QCD and comparison with O(N) models

The chiral transition for two-flavor QCD is predicted to be in the same universality class as the 3d O(4) model. This prediction is verified in the Wilson case, but not for the staggered-fermion case. The comparison is usually done assuming infinite-volume behavior. Here we make an analysis of existing staggered-fermion data using finite-size scaling and normalizing the QCD data. We find better agreement for larger quark masses.

hep-lat↗