SU(2) potentials from large lattices

Booth, Stephen; Hulsebos, Arjan; Irving, A.C.; McKerrell, A.; Michael, C.; Spencer, P.S.; Stephenson, P.

doi:10.1016/0550-3213(93)90023-i

Cited by 40 publications

(44 citation statements)

References 17 publications

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“…The OA data gives a smaller lattice spacing, so that is the more conservative choice, although averaging the lattice spacing obtained from the two datasets would probably make more sense, since they are likely extremes of the rotational non-invariance. Also shown is Wilson-action OA data of the UKQCD collaboration [19] for β = 2.85, with the lattice spacing scaled for best fit at R = 5a, which gives a factor of 0.98, the β = 2.85 lattice spacing being slightly larger than that of the monopole-suppressed simulation (but the same within errors). Our 60 4 lattice is therefore physically slightly larger than that of the UKQCD simulation (48 3 × 56), so there is little worry that the lattice is too small to access a region where confinement should easily be seen, if there.…”

Section: Lattice Coulomb Potentialmentioning

confidence: 99%

“…About one PC-year of computing time was devoted to the above study. At least two PC-years were devoted to determining the interquark potential using a more standard smeared op-erator method [19,20]. The latter simulations were done on a 40 4 lattice with ordinary periodic boundary conditions and no gauge fixing.…”

Section: Interquark Potentialmentioning

confidence: 99%

“…Three different smearing levels (5, 10 and 20 iterations) were generated using the recursive blocking scheme which replaces links with a combination of the original link and U-bends. A straight-link weight of c = 2 as defined in [19] was used. Wilson loops with both like and unlike operators at the ends were measured resulting in six different types of loops.…”

Section: Interquark Potentialmentioning

confidence: 99%

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Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Grady

2013

Nuclear Physics B

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Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)-Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb-gauge methods, with an infinite lattice critical point near β = 3.2. The theory with both Z2 vortices and monopoles and SO(3)-Z2 monopoles eliminated is simulated in the strong coupling (β = 0) limit on lattices up to 60 4 . Here, as in the high-β phase of the Wilson action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β. Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α ∼ 1.4. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.

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Section: Lattice Coulomb Potentialmentioning

confidence: 99%

Section: Interquark Potentialmentioning

confidence: 99%

Section: Interquark Potentialmentioning

confidence: 99%

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Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Grady

2013

Nuclear Physics B

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“…with [12] a(β = 2.70)/a(β = 2.85) = 1.6. The fact that the dip is less pronounced at β = 2.7 than at the higher value of β, is, most likely, not due to a statistical fluctuation.…”

Section: Density Of Spikesmentioning

confidence: 99%

Gauge singularities in the SU(2) vacuum on the lattice

Gutbrod

2005

Nuclear Physics B

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I summarize and extend the qualitative results, obtained previously by inspection of SU(2) lattice gauge field configurations. These configurations were generated by the Wilson action, then transformed to a Landau gauge and smoothed by Fourier filtering. This leads to sharp peaks in field strengths and related quantities, the characteristics of which are very well separated from a background. These spikes are caused by gauge singularities, Their densiis determined as 1.5/fm 4 , with very good scaling properties as a function of the bare coupling constant. The number of spikes within a configuration vanishes when approaching the deconfinement region. Furthermore, the Landau-gauging procedure becomes unique, if the probability to find a spike is much smaller than unity. The relation of the spikes to the instantons obtained by cooling is investigated. Finally, a correlation between the presence of spikes and the infrared behaviour of the gluon propagator is demonstrated.

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“…This takes into account at least the tree-level lattice artifacts. Also, since recent Monte Carlo data [5,6,7] on fine lattices are accurate enough to see that e really is a running charge, Michael [5] proposed to take this into account in a phenomenological way by replacing e with e − f /r, with some new parameter f . If necessary, we will distinguish these kind of ansätze from the naive Coulomb + linear one, by calling them "modified Coulomb + linear ansätze" (or fits).…”

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confidence: 99%

QCD (lattice) potential and coupling: How to accurately interpolate between multiloop QCD and the string picture

Klassen

1995

Phys. Rev. D

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We present a simple parameterization of the running coupling constant α V (q), defined via the static potential, that interpolates between 2-loop QCD in the UV and the string prediction V (r) = σr − π 12r in the IR. Besides the usual Λ-parameter and the string tension σ, α V (q) depends on one dimensionless parameter, determining how fast the crossover from UV to IR behavior occurs (in principle we know how to take into account any number of loops by adding more parameters). Using a new ansatz for the lattice potential in terms of the continuum α V (q), we can fit quenched and unquenched Monte Carlo results for the potential down to one lattice spacing, and at the same time extract α V (q) to high precision. We compare our ansatz with 1-loop results for the lattice potential, and use α V (q) from our fits to quantitatively check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine Sommer's scale r 0 much more accurately than previously possible. For pure SU(3) we find that α V (q) scales on the percent level for β ≥ 6.

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SU(2) potentials from large lattices

Cited by 40 publications

References 17 publications

Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory

Gauge singularities in the SU(2) vacuum on the lattice

QCD (lattice) potential and coupling: How to accurately interpolate between multiloop QCD and the string picture

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