Monopole clusters and critical dynamics in four-dimensional U(1)

Bode, Achim; Lippert, Th.; Schilling, Klaus

doi:10.1016/0920-5632(94)90443-x

Cited by 18 publications

(21 citation statements)

References 4 publications

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“…Results were presented in support of this view by switching to spherical lattices with trivial homotopy group where such wrapping loops are no more topologically stabilized [26,27,28,29]. But on spherical lattices equivalent to L = 26 at γ = −0.2, double peak structures have recently been reported to reappear [20,21], corroborating earlier observations with periodic boundary conditions at γ = 0: the suppression of monopole loop penetration through the lattice surface turned out to be incapable of preventing the incriminated double peak signal to show up on large lattices, to say L = 32 [30,31,32].…”

Section: Introductionsupporting

confidence: 71%

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

Arnold¹,

Schilling

Lippert

1999

Phys. Rev. D

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We demonstrate that substantial progress can be achieved in the study of the phase structure of 4-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms, through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. We estimate that the creation of adequate samples (with order 100 flip-flops) becomes a matter of half a year's runtime at 2 Gflops sustained performance for lattices of size up to 244 .

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Section: Introductionsupporting

confidence: 71%

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

Arnold¹,

Schilling

Lippert

1999

Phys. Rev. D

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“…But the issue is important, as whatever is interesting in the compact lattice QED is essentially related to the monopoles: The phase transition itself is known to be associated with the occurence of magnetic monopoles being topological excitations of the theory [6][7][8]. Modifications of the monopole contribution to the action have appreciable consequences for its position [9] and properties [10]. The long distance force in the confinement phase [11,12] and the chiral symmetry breaking [13] are best understood in terms of the monopole condensate.…”

Section: Introductionmentioning

confidence: 99%

Scaling analysis of the magnetic monopole mass and condensate in the pure U(1) lattice gauge theory

1999

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We observe the power law scaling behavior of the monopole mass and condensate in the pure compact U(1) gauge theory with the Villain action. In the Coulomb phase the monopole mass scales with the exponent νm = 0.49(4). In the confinement phase the behavior of the monopole condensate is described with remarkable accuracy by the exponent βexp = 0.197(3). Possible implications of these phenomena for a construction of a strongly coupled continuum U(1) gauge theory are discussed.

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“…The large (infrared) clusters which percolate through the lattice and wrap around the boundaries of lattice are formed by the longest monopole loop L loops . The method of numerical computations of the monopole world line in four dimension is explained in [16]. If the physical lattice volume is large enough, the small clusters and the large clusters are separated.…”

Section: Zero Modes Of Overlap Fermions Instantons and Monopoles Mamentioning

confidence: 99%

Zero modes of overlap fermions, instantons and monopoles

Giacomo¹,

Hasegawa²

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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The purpose of this study is to investigate the relations between instantons, monopoles, and Chiral symmetry breaking. The monopoles are important topological configurations existing in QCD which are believed to produce colour confinement. The groups of University of Kanazawa and Pisa have produced by Lattice simulations many results supporting the idea that QCD vacuum is a dual superconductor. Instantons are related to Chiral symmetry breaking, as explained e.g. in the instanton liquid model of E. V. SHURYAK. Clarifying quantitatively the relation between monopoles and instantons is not easy, also because monopoles are three dimensional objects, while instantons are four dimensional. We generate configurations, adding monopoleantimonopole pairs of opposite charges by a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops in the configurations. Then, we count the number of fermion zero modes in the configurations using Overlap fermions as a tool. Finally, we find that one monopole-antimonopole pair makes one zero mode of plus or minus chirality, that is to say, one instanton of plus or minus charge.

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Monopole clusters and critical dynamics in four-dimensional U(1)

Cited by 18 publications

References 4 publications

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

Scaling analysis of the magnetic monopole mass and condensate in the pure U(1) lattice gauge theory

Zero modes of overlap fermions, instantons and monopoles

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