A new method for updating SU(N) matrices in computer simulations of gauge theories

Cabibbo, N.; Marinari, Enzo

doi:10.1016/0370-2693(82)90696-7

Cited by 501 publications

(414 citation statements)

References 4 publications

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“…In our calculations of the magnetic-monopole current configuration, we fix the center on the origin 154) and change the value of ρ. The results are summarized in Table 1 and Fig.…”

Section: One Instantons and Magnetic Monopole Loops On The Latticementioning

confidence: 99%

“…First, we generate gauge field configurations of link variables {U x,µ } on a four-dimensional Euclidean lattice L ǫ = (ǫZ) 4 with a lattice spacing ǫ by using the standard method: the Wilson action based on the heat bath method for G = SU(2), the Wilson action based on the pseudo heat-bath method [154] for G = SU(3).…”

Section: Lattice Reduction Condition and Color Fieldmentioning

confidence: 99%

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Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the YangMills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator.Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gaugeinvariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations.However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability 1 groupH of G, while there is a unique option ofH = U(1) for G = SU(2). The maximal stability group depends...

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“…In our calculations of the magnetic-monopole current configuration, we fix the center on the origin 154) and change the value of ρ. The results are summarized in Table 1 and Fig.…”

Section: One Instantons and Magnetic Monopole Loops On The Latticementioning

confidence: 99%

Section: Lattice Reduction Condition and Color Fieldmentioning

confidence: 99%

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

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“…Quenched simulations are performed using the standard mix of Brown -Woch microcanonical over-relaxation [33] and Cabibbo -Mari-nari heat bath updates [34], performed on all N(N − 1)/2 SU(2) subgroups of the SU(N) link variables. It is known that simulations performed on SU(2) subgroups suffer critical slowing down at larger N, but the largest N is only 7 and this problem did not appear.…”

mentioning

confidence: 99%

Lattice baryons in the1/Nexpansion

DeGrand

2012

Phys. Rev. D

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“…The canonical ensemble of gauge field configurations was generated using a combination of microcanonical over-relaxation (MOR) [9] and quasi-heat-bath (QHB) algorithms [10]. An individual MOR or QHB step consisted of updating consecutively the three 2 × 2 submatrices of the SU(3) link variable [11]. In our implementation five MOR steps were followed by two QHB ones.…”

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confidence: 99%

A quark-antiquark condensate in three-dimensional QCD

Damgaard¹,

Heller²,

Krasnitz³

et al. 1998

Physics Letters B

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Three-dimensional lattice QCD is studied by Monte Carlo simulations within the quenched approximation. At zero temperature a quark-antiquark condensate is observed in the limit of vanishing quark masses. The condensate vanishes continuously at the finite-temperature deconfinement phase transition of the theory. A natural interpretation of this phenomenon in the full theory with dynamical quarks is in terms of the spontaneous flavor symmetry breakingIn addition, the spectrum of low-lying Dirac operator eigenvalues is computed and found to be consistent with a flat distribution at zero temperature, in agreement with analytical predictions.NBI-HE-98-06 FSU-SCRI-98-28 UALG/TP/98-4 hep-lat/9803012

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A new method for updating SU(N) matrices in computer simulations of gauge theories

Cited by 501 publications

References 4 publications

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

Lattice baryons in the1/Nexpansion

A quark-antiquark condensate in three-dimensional QCD

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