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Tereza Mendes

Publications and source records attributed to Tereza Mendes.

87 records · Page 5Linked to original sources
arXiv2001

SU(2) Running Coupling Constant and Confinement in Minimal Coulomb and Landau Gauges

We present a numerical study of the space-space and time-time components of the gluon propagator at equal time in the minimal Coulomb gauge, and of the gluon and ghost propagators in the minimal Landau gauge. This work allows a non-perturbative evaluation of the running coupling constant and a numerical check of Gribov's confinement scenarios for these two gauges. Our simulations are done in pure SU(2) lattice gauge theory at $β= 2.2$. We consider several lattice volumes in order to control finite-volume effects and extrapolate our results to infinite lattice volume.

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arXiv1999

Numerical evidence for Goldstone-mode effects in the three-dimensional O(4)-model

We investigate the three-dimensional O(4)-model on 24^3--96^3 lattices as a function of the magnetic field H. Below the critical point, in the broken phase, we confirm explicitly the H^{1/2} dependence of the magnetization and the corresponding H^{-1/2} divergence of the longitudinal susceptibility, which are predicted from the existence of Goldstone modes. At the critical point the magnetization follows the expected finite-size-scaling behavior, with critical exponent delta = 4.87(1).

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arXiv1999

Gauge fixing and gluon propagator in lambda-gauges

We discuss critical slowing-down of several gauge-fixing algorithms for the so-called lambda-gauges in the SU(2) case at zero temperature. For these gauges we also evaluate the gluon propagator using different definitions of the lattice gluon field, corresponding to discretization errors of different orders.

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arXiv1998

Pseudo-Character Expansions for U(N)-Invariant Spin Models on CP^{N-1}

We define a set of orthogonal functions on the complex projective space CP^{N-1}, and compute their Clebsch-Gordan coefficients as well as a large class of 6-j symbols. We also provide all the needed formulae for the generation of high-temperature expansions for U(N)-invariant spin models defined on CP^{N-1}.

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arXiv1998

Effects of Nonperturbative Improvement in Quenched Hadron Spectroscopy

We discuss a comparative analysis of unimproved and nonperturbatively improved quenched hadron spectroscopy, on a set of 104 gauge configurations, at beta=6.2. We also present here our results for meson decay constants, including the constants f_D and f_Ds in the charm-quark region.

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arXiv1997

1) The Influence of Gribov Copies on Gluon and Ghost Propagators in Landau Gauge and 2) A New Implementation of the Fourier Acceleration Method

We study the influence of Gribov copies on gluon and ghost propagators in lattice Landau gauge. For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy. On the contrary, for the ghost propagator, Gribov noise is clearly observable, at least in the strong- coupling regime. We also observe, in the limit of large lattice volume, a gluon propagator decreasing as the momentum goes to zero. Finally, we introduce an implementation of the method of Fourier Acceleration which avoids the use of the fast Fourier transform, being well suited for parallel and vector machines. We apply it to the case of Landau gauge fixing, and study its performance on APE computers.

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arXiv1996

Critical Slowing-Down in $SU(2)$ Landau Gauge-Fixing Algorithms

We study the problem of critical slowing-down for gauge-fixing algorithms (Landau gauge) in $SU(2)$ lattice gauge theory on a $2$-dimensional lattice. We consider five such algorithms, and lattice sizes ranging from $8^{2}$ to $36^{2}$ (up to $64^2$ in the case of Fourier acceleration). We measure four different observables and we find that for each given algorithm they all have the same relaxation time within error bars. We obtain that: the so-called {\em Los Alamos} method has dynamic critical exponent $z \approx 2$, the {\em overrelaxation} method and the {\em stochastic overrelaxation} method have $z \approx 1$, the so-called {\em Cornell} method has $z$ slightly smaller than $1$ and the {\em Fourier acceleration} method completely eliminates critical slowing-down. A detailed discussion and analysis of the tuning of these algorithms is also presented.

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arXiv1996

Study of Critical Slowing-Down in $SU(2)$ Landau Gauge Fixing

We study the problem of critical slowing-down for gauge-fixing algorithms (Landau gauge) in $SU(2)$ lattice gauge theory on $2$ and $4$ dimensional lattices, both numerically and analytically. We consider five such algorithms, and we measure four different observables. A detailed discussion and analysis of the tuning of these algorithms is also presented.

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arXiv1996

Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and Two-Dimensional $O(N)$-Symmetric Nonlinear $σ$-Models

We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $σ$-models. We then apply the method to the two-dimensional $O(N)$-symmetric nonlinear $σ$-models (also called $N$-vector models) with $N=3,4,8$ and study its dynamic critical behavior. Using lattices up to $256 \times 256$, we find dynamic critical exponents $z_{int,{\cal M}^2} \approx 0.70 \pm 0.08$, $0.60 \pm 0.07$, $0.52 \pm 0.10$ for $N=3,4,8$, respectively (subjective 68\% confidence intervals). Thus, for these asymptotically free models, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated; and the dynamic critical exponent does apparently vary with $N$. We also analyze the static data for $N=8$ using a finite-size-scaling extrapolation method. The correlation length $ξ$ agrees with the four-loop asymptotic-freedom prediction to within $\approx 1\%$ over the interval $12 < ξ< 650$.

hep-lat↗
arXiv1995

Application of the $O(N)$-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional $σ$-Models and to the Generation of High-Temperature Expansions in Higher Dimensions

In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these results are obtained using a high-temperature expansion in terms of hyperspherical harmonics. Applications in higher dimensions of the same technique are then discussed.

hep-lat↗
arXiv1995

Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional $N$-Vector Model for $N=3,4,8$

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N = 3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.

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arXiv1995

Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $σ$-Models

We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear $σ$-models: it is based on embedding an $XY$ model into the given $σ$-model, and then updating the induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional $O(N)$ $σ$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We find that the dynamic critical exponent $z$ varies systematically between these different asymptotically free models: it is approximately 0.70 for $O(3)$, 0.60 for $O(4)$, 0.50 for $O(8)$, and 0.45 for $SU(3)$. It goes without saying that we have no theoretical explanation of this behavior.

hep-lat↗
arXiv1995

Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models

We solve exactly the general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical harmonics. The possible continuum limits are discussed for a general one-parameter family of interactions, and an infinite number of universality classes is found. For these classes we compute the finite-size-scaling functions and the leading corrections to finite-size scaling. A special two-parameter family of interactions (which includes the mixed isovector/isotensor model) is also treated, and no additional universality classes appear. In the appendices we give new formulae for the Clebsch-Gordan coefficients and 6--$j$ symbols of the $O(N)$ group, and some new generalizations of the Poisson summation formula; these may be of independent interest.

hep-lat↗
arXiv1995

Multi-Grid Monte Carlo. IV. One-Dimensional $O(4)$-Symmetric Nonlinear $σ$-Model

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation and a W-cycle, applied to the one-dimensional $O(4)$-symmetric nonlinear $σ$-model [= $SU(2)$ principal chiral model], on lattices from $L=128$ to $L=16384$. Our data for the integrated autocorrelation time $τ_{int,{\cal M}^2}$ are well fit by a logarithmic growth. We have no idea why the critical slowing-down is not completely eliminated.

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