A Python program for the implementation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml28" display="inline" overflow="scroll" altimg="si28.gif"><mml:mi>Γ</mml:mi></mml:math>-method for Monte Carlo simulations

Palma, Barbara De; Erba, Marco; Mantovani, Luca; Mosco, Nicola

doi:10.1016/j.cpc.2018.07.004

Cited by 14 publications

(11 citation statements)

References 7 publications

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“…In order to give a reliable estimate of the observable's uncertainty we need to take these autocorrelations into account. For this work we have used the Γ-method [29,30] to estimate the autocorrelation time, τ int and, from it, an appropriate bin size to obtain statistically independent samples. Since autocorrelations are observable-dependent we have computed τ int of ∆α had for the light and strange flavours on each ensemble at different energies.…”

Section: Autocorrelation Studymentioning

confidence: 99%

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

Cè¹,

José²,

Gérardin³

et al. 2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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Section: Autocorrelation Studymentioning

confidence: 99%

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

Cè¹,

José²,

Gérardin³

et al. 2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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“…On the a15m135XL we have measuredψψ only on every saved configuration for the first half of each stream, while we measured it at each accept/reject step for the second half. The integrated autocorrelation time, as well as the average and statistical errors ofψψ, are computed using the Γmethod analysis [107] with the Python package UNEW [108]. We report the results in Table IX.…”

Section: Appendix C: Hmc For New Ensemblesmentioning

confidence: 99%

FK/Fπ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

et al. 2020

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We report the results of a lattice quantum chromodynamics calculation of F K =F π using Möbius domain-wall fermions computed on gradient-flowed N f ¼ 2 þ 1 þ 1 highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from 130 ≲ m π ≲ 400 MeV, four lattice spacings of a ∼ 0.15, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the a ∼ 0.06 fm ensemble is helpful, but not necessary to achieve a subpercent determination of F K =F π. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of FKþ =Fˆπþ ¼ 1.1942ð45Þ with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of jV us j=jV ud j ¼ 0.2311ð10Þ.

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“…The numerical computation of this sum requires some care and standard methods exist to optimize the integration range, in order to minimize the final error [47,48]. We used the Python implementation described in [49], that is freely available under the MIT License. However, probably the most straightforward and practical procedure is to use the relation [4,50]…”

Section: Discretizationmentioning

confidence: 99%

Topological critical slowing down: Variations on a toy model

Bonati

D’Elia

2018

Phys. Rev. E

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Numerical simulations of lattice quantum field theories whose continuum counterparts possess classical solutions with nontrivial topology face a severe critical slowing down as the continuum limit is approached. Standard Monte Carlo algorithms develop a loss of ergodicity, with the system remaining frozen in configurations with fixed topology. We analyze the problem in a simple toy model, consisting of the path integral formulation of a quantum mechanical particle constrained to move on a circumference. More specifically, we implement for this toy model various techniques which have been proposed to solve or alleviate the problem for more complex systems, like non-Abelian gauge theories, and compare them both in the regime of low temperature and in that of very high temperature. Among the various techniques, we propose an alternative algorithm which completely solves the freezing problem, but unfortunately is specifically tailored for this particular model and not easily exportable to more complex systems.

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A Python program for the implementation of the Γ-method for Monte Carlo simulations

Cited by 14 publications

References 7 publications

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

FK/Fπ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles

Topological critical slowing down: Variations on a toy model

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