Finite size scaling analysis of compact QED

Arnold, Guido; Lippert, Th.; Schilling, Klaus; Neuhaus, T.

doi:10.1016/s0920-5632(01)01001-5

Cited by 22 publications

(35 citation statements)

References 8 publications

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“…Our results are summarised in Tab. 2 with a comparison with the values in [31]. Once again, the agreement testify the good ergodic properties of the algorithm.…”

Section: Numerical Investigation Of the Phase Transitionsupporting

confidence: 56%

“…[21][22][23][24][25][26][27][28][29][30]). The issue was cleared only relatively recently, with investigations that made a crucial use of supercomputers [31,32]. What makes the transition difficult to observe numerically is the role played in the deconfinement phase transition by magnetic monopoles [33], which condense in the confined phase [33,34].…”

Section: The Modelmentioning

confidence: 99%

“…Once again, the agreement testify the good ergodic properties of the algorithm. Using our L β c (L) present method β c (L) reference values 8 1.00744(2) 1.00741 (1) [31].…”

Section: Numerical Investigation Of the Phase Transitionmentioning

confidence: 99%

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An efficient algorithm for numerical computations of continuous densities of states

et al. 2016

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In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard integration. In this work, our recently introduced method in this class (the LLR approach) is analysed and further developed. Our approach is a histogram free method particularly suited for systems with continuous degrees of freedom giving rise to a continuum density of states, as it is commonly found in Lattice Gauge Theories and in some Statistical Mechanics systems. We show that the method possesses an exponential error suppression that allows us to estimate the density of states over several orders of magnitude with nearly-constant relative precision. We explain how ergodicity issues can be avoided and how expectation values of arbitrary observables can be obtained within this framework. We then demonstrate the method using Compact U(1) Lattice Gauge Theory as a show case. A thorough study of the algorithm parameter dependence of the results is performed and compared with the analytically expected behaviour. We obtain high precision values for the critical coupling for the phase transition and for the peak value of the specific heat for lattice sizes ranging from 8 4 to 20 4 . Our results perfectly agree with the reference values reported in the literature, which covers lattice sizes up to 18 4 . Robust results for the 20 4 volume are obtained for the first time. This latter investigation, which, due to strong metastabilities developed at the pseudo-critical coupling of the system, so far has been out of reach even on supercomputers with importance sampling approaches, has been performed to high accuracy with modest computational resources. This shows the potential of the method for studies of first order phase transitions. Other situations where the method is expected to be superior to importance sampling techniques are pointed out.

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“…Our results are summarised in Tab. 2 with a comparison with the values in [31]. Once again, the agreement testify the good ergodic properties of the algorithm.…”

Section: Numerical Investigation Of the Phase Transitionsupporting

confidence: 56%

Section: The Modelmentioning

confidence: 99%

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An efficient algorithm for numerical computations of continuous densities of states

et al. 2016

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“…Using the Wilson action, this transition can be shown to be of first order (with very long correlation length) and located, in the thermodynamic limit, at β c ≈ 1.011 (for recent high precision measurements of the transition point see [7]). It is this order parameter, a monopole creation operator, that allows to rigorously distinguish between the Confined and the Coulomb phases of U(1)lgt.…”

Section: Introductionmentioning

confidence: 99%

“…This model has two phases: a confined phase at strong coupling and a Coulomb phase at weak coupling. The order and the location of the phase transition that separate them depend on the action form and has been a long standing subject of debate [5,6,7,8]. The idea that monopoles could play a crucial role in the description of confinement appeared after the inspiring work of Polyakov [9] in three dimensions and the contemporary conjecture, known as dual superconductivity (DS), by Mandelstam and 't Hooft about confinement in QCD [10,11].…”

Section: Introductionmentioning

confidence: 99%

Monopole–antimonopole correlation functions in 4D U(1) gauge theory

Tagliacozzo

2006

Physics Letters B

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We study the two-point correlator of a modified Confined-Coulomb transition order parameter in four dimensional compact U (1) lattice gauge theory with Wilson action. Its long distance behavior in the confined phase turns out to be governed by a single particle decay. The mass of this particle is computed and found to be in agreement with previous calculations of the 0 ++ gaugeball mass. Remarkably, our order parameter allows to extract a good signal to noise ratio for masses with low statistics. The results we present provide a numerical check of a theorem about the structure of the Hilbert space describing the confined phase of four dimensional compact U (1) lattice gauge theories.

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