arXiv subjects

Attilio Cucchieri

Publications and source records attributed to Attilio Cucchieri.

83 records · Page 5Linked to original sources

arXiv1998

Numerical Study of the Gluon Propagator in Lattice Landau Gauge: the Three-Dimensional Case

We study the infrared behavior of the gluon propagator in lattice Landau gauge, for pure SU(2) lattice gauge theory in a three-dimensional lattice. Simulations are done for nine different values of the coupling $β$, from $β= 0$ (strong coupling) to $β= 6.0$ (in the weak-coupling region). In the limit of large lattice volumes, we observe in all cases a gluon propagator decreasing as the momentum goes to zero.

hep-lat↗

arXiv1997

Numerical Study of the Fundamental Modular Region in the Minimal Landau Gauge

We study numerically the so-called fundamental modular region Lambda, a region free of Gribov copies, in the minimal Landau gauge for pure SU(2) lattice gauge theory. To this end we evaluate the influence of Gribov copies on several quantities --- such as the smallest eigenvalue of the Faddeev-Popov matrix, the third and the fourth derivatives of the minimizing function, and the so-called horizon function --- which are used to characterize the region Lambda. Simulations are done at four different values of the coupling: beta = 0, 0.8, 1.6, 2.7, and for volumes up to 16^4. We find that typical (thermalized and gauge-fixed) configurations, including those belonging to the region Lambda, lie very close to the Gribov horizon $\partial Ω$, and are characterized, in the limit of large lattice volume, by a negative-definite horizon tensor.

hep-lat↗

arXiv1997

Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and Ghost Propagators

We study the influence of Gribov copies on gluon and ghost propagators, evaluated numerically in pure SU(2) lattice gauge theory in the minimal Landau gauge. Simulations are done at four different values of $β$ (namely $β$ = 0, 0.8, 1.6 and 2.7) and for volumes up to $16^4$ (up to $24^4$ at $β$ = 1.6). For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy, even at very small values of the coupling $β$. On the contrary, for the ghost propagator, Gribov noise is clearly observable for the three values of $β$ in the strong-coupling regime. In particular, data corresponding to the minimal Landau gauge are always smaller than those obtained in a generic Landau gauge. This result can be qualitatively explained.

hep-lat↗

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.

hep-lat↗

arXiv1997

Infrared Behavior of the Gluon Propagator in Lattice Landau Gauge

We evaluate numerically the four-momentum-space gluon propagator in lattice Landau gauge, for pure SU(2) lattice gauge theory with periodic boundary conditions. Simulations are done in the strong-coupling regime, namely at $β= 0, 0.8, 1.2 and 1.6$, and for lattice sizes up to $30^4, 16^4, 20^4 and 24^4$ respectively. In the limit of large lattice volume, we observe in all cases a gluon propagator decreasing as the momentum goes to zero. This counter-intuitive result has a straightforward interpretation as resulting from the proximity of the so-called first Gribov horizon in infrared directions.

hep-lat↗

arXiv1997

Static Color-Coulomb Force

The static color-Coulomb interaction potential is calculated as the solution of a non-linear integral equation which arises in the Hamiltonian Coulomb gauge when the restriction to the interior of the Gribov horizon is implemented. The potential obtained is in qualitative agreement with expectations, being Coulombic with logarithmic corrections at short range, and confining at long range. The values obtained for the string tension and $Λ_{\overline{MS}}$ are in semi-quantitative agreement with lattice Monte Carlo and phenomenological determinations.

hep-th↗

arXiv1996

Color-Coulomb Force Calculated from Lattice Coulomb Hamiltonian

The static color-Coulomb potential is calculated as the solution of a non-linear integral equation. This equation has been derived recently as a self-consistency condition which arises in the Coulomb Hamiltonian formulation of lattice gauge theory when the restriction to the interior of the Gribov horizon is implemented. The potential obtained is in qualitative agreement with expectations, being Coulombic with logarithmic corrections at short range and confining at long range. The values obtained for the string tension and $Λ_{\overline{MS}}$ are in semi-quantitative agreement with lattice Monte Carlo and phenomenological determinations.

hep-th↗

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.

hep-lat↗

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.

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

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↗