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Robert G. Edwards

Publications and source records attributed to Robert G. Edwards.

125 records · Page 7Linked to original sources
arXiv1997

SCRI Results With the Tadpole-Improved Clover Action

We compare light hadron spectroscopy using the Wilson and Clover fermionic actions. We show that a Clover coefficient chosen using tadpole-improved tree-level perturbation theory effectively eliminates the O(a) discretization errors present in the Wilson action. We find that discretization errors in light spectroscopy for both the Wilson and Clover actions are characterized by an energy scale mu of about 200-300 MeV, indicating that these errors can be reduced to the 5% level by using the Clover action at an inverse lattice spacing of about 1.3 GeV.

hep-lat↗
arXiv1997

QCDSP - A status report

The QCDSP machine at Columbia University has grown to 2,048 nodes achieving a peak speed of 100 Gigaflops. Software for quenched and Hybrid Monte Carlo (HMC) evolution schemes has been developed for staggered fermions, with support for Wilson and clover fermions under development. We provide an overview of the runtime environment, the current status of the QCDSP construction program and preliminary results not presented elsewhere in these proceedings.

hep-lat↗
arXiv1996

Comparing Wilson and Clover Quenched $SU(3)$ Spectroscopy with an Improved Gauge Action

We present results of quenched $SU(3)$ hadron spectroscopy comparing $\order(a)$ improved Wilson (Clover) fermions with conventional Wilson fermions. The configurations were generated using an $\order(a^2)$ improved 6-link $SU(3)$ pure gauge action at $β$'s corresponding to lattice spacings of $0.15$, $0.18$, $0.20$, $0.33$, and $0.43$ fm. We find evidence that fermionic scaling violations are consistent with $\order(a^2)$ for Clover and $\order(a)$ with a nonnegligible $\order(a^2)$ term for standard Wilson fermions. This latter mixed ansatz makes a reliable continuum extrapolation problematic for Wilson fermions. We also find that the slope of the scaling violations is roughly $250 MeV$ for both Wilson and Clover fermions.

hep-lat↗
arXiv1995

A Comparison of Clover and Wilson Spectroscopy in the Presence of Dynamical Quarks

We present preliminary results of light hadron spectroscopy using valence, tadpole-improved, Clover fermions on an ensemble of gauge configurations generated with 2 flavors of staggered fermions at a beta of 5.6. We compare the slope and intercept of the curve M_V vs. M_PS^2 for Clover and Wilson fermions. We show that a higher order chiral perturbation theory ansatz works very well for chiral extrapolations.

hep-lat↗
arXiv1995

Quenched $SU(3)$ hadron spectroscopy using improved fermionic and gauge actions

We present results of quenched $SU(3)$ hadron spectroscopy using $\order(a)$ improved Wilson fermions. The configurations were generated using an $\order(a^2)$ improved 6-link $SU(3)$ pure gauge action at $β$'s corresponding to lattice spacings of $0.43$, $0.25$, $0.20$, $0.18$, and $0.15$ fm. We find evidence that fermionic scaling violations are consistent with $\order(a^2)$ errors.

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.

hep-lat↗
arXiv1994

Cooling in QCD Spectroscopy

We test the cooling algorithm with gluonic and staggered hadronic spectroscopy on $SU(3)$ gauge field configurations generated with two flavors of staggered dynamical fermions. We find cooling is not reliable as the basis for improved hadronic operators. We also find that performing cooling sweeps to reveal more clearly the topological properties of the gauge fields eliminates the spin structure of the hadron spectrum.

hep-lat↗
arXiv1994

New Method for the Extrapolation of Finite-Size Data to Infinite Volume

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $σ$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

hep-lat↗
arXiv1994

Two-Dimensional $O(3)$ $σ$-Model up to Correlation Length $10^5$

We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $σ$-model at correlation lengths $ξ$ up to $\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is $\approx 25\%$ at $ξ\sim 10^2$, decreases to $\approx 4\%$ at $ξ\sim 10^5$.

hep-lat↗
arXiv1994

Asymptotic Scaling in the Two-Dimensional $O(3)$ $σ$-Model at Correlation Length $10^5$

We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $σ$-model at correlation lengths $ξ$ up to $\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is $\approx 25\%$ at $ξ\sim 10^2$, decreases to $\approx 4\%$ at $ξ\sim 10^5$.

hep-lat↗
arXiv1994

Finite-Size Scaling at $ξ/L \gg 1$

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $σ$-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

hep-lat↗
arXiv1993

New Universality Classes for Two-Dimensional $σ$-Models

We argue that the two-dimensional $O(N)$-invariant lattice $σ$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $σ$-model constructed by conventional perturbation theory. We test the proposed scenario with a high-precision Monte Carlo simulation for $N=3,4$ on lattices up to $512 \times 512$, using a Wolff-type embedding algorithm. [CPU time $\approx$ 7 years IBM RS-6000/320H] The finite-size-scaling data confirm the existence of the predicted new family of continuum limits. In particular, the $RP^{N-1}$ and $N$-vector models do not lie in the same universality class.

hep-lat↗
arXiv1992

On the Dynamics of Light Quarks in QCD

We describe recent results concerning the behavior of lattice QCD with light dynamical Wilson and Staggered quarks. We show that it is possible to reach regions of parameter space with light pions $m_π\approx 0.2/a$ using Wilson fermions. If the Hybrid Molecular Dynamics (HMD) algorithm is used with the same parameters it gives incorrect results. We also present preliminary results using a higher-order integration scheme.

hep-lat↗
arXiv1992

Wolff-Type Embedding Algorithms for General Nonlinear $σ$-Models

We study a class of Monte Carlo algorithms for the nonlinear $σ$-model, based on a Wolff-type embedding of Ising spins into the target manifold $M$. We argue heuristically that, at least for an asymptotically free model, such an algorithm can have dynamic critical exponent $z \ll 2$ only if the embedding is based on an (involutive) isometry of $M$ whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a discrete quotient of a product of spheres. Numerical simulations of the idealized codimension-2 algorithm for the two-dimensional $O(4)$-symmetric $σ$-model yield $z_{int,{\cal M}^2} = 1.5 \pm 0.5$ (subjective 68\% confidence interval), in agreement with our heuristic argument.

hep-lat↗
arXiv1992

Multi-Grid Monte Carlo III. Two-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 applied to the two-dimensional O(4)-symmetric nonlinear $σ$-model [= SU(2) principal chiral model], on lattices up to $256 \times 256$. We find a dynamic critical exponent $z_{int,{\cal M}^2} = 0.60 \pm 0.07$ for the W-cycle and $z_{int,{\cal M}^2} = 1.13 \pm 0.11$ for the V-cycle, compared to $z_{int,{\cal M}^2} = 2.0 \pm 0.15$ for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a $256 \times 256$ lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

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