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Title: Scaling properties of multiscale equilibration

Abstract

We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on nontopological long-distance observables in pure SU (3) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.

Authors:
;
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1433463
Alternate Identifier(s):
OSTI ID: 1501513
Grant/Contract Number:  
SC0010495; SC0011090; SC0018121
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 7; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Particles & Fields; Statistical Physics

Citation Formats

Detmold, W., and Endres, M. G. Scaling properties of multiscale equilibration. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.074507.
Detmold, W., & Endres, M. G. Scaling properties of multiscale equilibration. United States. doi:10.1103/PhysRevD.97.074507.
Detmold, W., and Endres, M. G. Tue . "Scaling properties of multiscale equilibration". United States. doi:10.1103/PhysRevD.97.074507.
@article{osti_1433463,
title = {Scaling properties of multiscale equilibration},
author = {Detmold, W. and Endres, M. G.},
abstractNote = {We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on nontopological long-distance observables in pure SU (3) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.},
doi = {10.1103/PhysRevD.97.074507},
journal = {Physical Review D},
number = 7,
volume = 97,
place = {United States},
year = {2018},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.074507

Figures / Tables:

TABLE I TABLE I: Ensemble parameters considered in this work. Note that the lattice spacings provided below are approximate and based on numerical estimates for w0.4/a, the physical value of the Sommer scale (taken to be $r$0 = 0.5 fm), and the continuum conversion factor between $r$0 and reference scale $w$0.4 determinedmore » in Ref. [27].« less

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    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.