Pure SU(2) lattice gauge theory on 324 lattices

Decker, Karsten M.; Forcrand, Philippe de

doi:10.1016/0920-5632(90)90315-l

Cited by 22 publications

(34 citation statements)

References 4 publications

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“…It is remarkable that T c in units of Λ MS differs only by less than 20% between SU (2) and SU (3) and also the corresponding value for QCD with four flavours, T c /Λ MS = 1.05 (20) [30], is surprisingly close to the SU (3) value.…”

Section: Scaling and Asymptotic Scalingmentioning

confidence: 55%

Scaling and asymptotic scaling in the SU(2) gauge theory

1993

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We determine the critical couplings for the deconfinement phase transition in SU (2) gauge theory on N τ × N 3 σ lattices with N τ = 8 and 16 and N σ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio T c / √ σ in the entire coupling regime β = 2.30 − 2.75, while the individual quantities still exhibit large scaling violations. We find T c / √ σ =0.69(2). We also discuss in detail the extrapolation of T c /Λ MS and √ σ/Λ MS to the continuum limit. Our result, which is consistent with the above ratio, is T c /Λ MS = 1.23(11) and √ σ/Λ MS = 1.79(12). We also comment upon corresponding results for SU (3) gauge theory and four flavour QCD.

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Section: Scaling and Asymptotic Scalingmentioning

confidence: 55%

Scaling and asymptotic scaling in the SU(2) gauge theory

1993

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“…This algorithm is able to speed up numerical simulations in the case of pure lattice gauge theory: in fact, an overall efficiency gain of up to a factor 10 has been observed [29] [for the SU(2) case] with respect to the heat-bath algorithm, and its dynamic critical exponent 10 has been found [31] to be equal to 1.0(1) [again in the SU (2) case]. The HOR algorithm is also easy to be implemented: m microcanonical (or energy-conserving) update sweeps are done, followed by one standard local ergodic update (heat-bath sweep) of the lattice.…”

Section: Numerical Simulations and Resultsmentioning

confidence: 99%

Gribov copies in the minimal Landau gauge: The influence on gluon and ghost propagators

1997

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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.Gauge theories, being invariant under local gauge transformations, are systems with redundant dynamical variables, which do not represent true dynamical degrees of freedom. The objects of interest are not the gauge fields themselves, but rather the classes (orbits) of gauge-related fields. The elimination of such redundant gauge degrees of freedom is essential for understanding and extracting physical information from these theories. This is usually done by a method called gauge fixing, which is based on the assumption that a gauge-fixing condition can be found which uniquely determines a representative gauge field on each orbit. It was pointed out by Gribov [1] that the standard gauge-fixing conditions used for perturbative calculations do not in fact fix the gauge fields uniquely: for a non-abelian gauge theory, in the Coulomb or in the Landau gauge, there are many gauge equivalent configurations satisfying the Coulomb or Landau transversality condition. The existence of these Gribov copies does not affect the results from perturbation theory, but their elimination could play a crucial role for non-perturbative features of these theories.One of the celebrated advantages of lattice gauge theories is that the lattice provides a regularization which makes the gauge group compact, so that the Gibbs average of any gauge-invariant quantity is well-defined and therefore gauge fixing is, in principle, not required. However, because

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“…In Table 1 we give λ and the derivative from Eq. (8), which up to a factor (-2) equals to the sum of derivatives. The latter is shown in Fig.…”

Section: Beta Function and Scaling In Su (2) Lattice Gauge Theorymentioning

confidence: 99%

“…The interpolation was checked further by a comparison of the coupling constant shift ∆β to MCRG measurements with scale two blocking transformations [7,8].…”

Section: Beta Function and Scaling In Su (2) Lattice Gauge Theorymentioning

confidence: 99%

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Scaling properties of the energy density in SU(2) lattice gauge theory

1995

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The lattice data for the energy density of SU (2) gauge theory are calculated with non-perturbative derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the non-perturbative beta function in accord with the measured critical temperature and ∆β−values and ii) a non-perturbative calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near T c . It is shown that at the critical temperature the energy density is scaling as a function of V T 3 with the corresponding 3d Ising model critical exponents. The value of ǫ(T c )/T 4 c in the continuum limit is estimated to be 0.256(23). In the high temperature regime the energy density is approaching its weak coupling limit from below, at T /T c ≈ 2 it has reached only about 70% of the limit.

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Pure SU(2) lattice gauge theory on 324 lattices

Cited by 22 publications

References 4 publications

Scaling and asymptotic scaling in the SU(2) gauge theory

Scaling and asymptotic scaling in the SU(2) gauge theory

Gribov copies in the minimal Landau gauge: The influence on gluon and ghost propagators

Scaling properties of the energy density in SU(2) lattice gauge theory

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