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Density of states method for symplectic gauge theories at finite temperature

Ed Bennett Orcid Logo, Biagio Lucini Orcid Logo, David Mason, Maurizio Piai Orcid Logo, Enrico Rinaldi Orcid Logo, Davide Vadacchino Orcid Logo

Physical Review D, Volume: 111, Issue: 11

Swansea University Authors: Ed Bennett Orcid Logo, Biagio Lucini Orcid Logo, David Mason, Maurizio Piai Orcid Logo

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DOI (Published version): 10.1103/physrevd.111.114511

Abstract

We study the finite-temperature behaviour of the Sp(4) Yang-Mills lattice theory in four di- mensions, by applying the Logarithmic Linear Relaxation (LLR) algorithm. We demonstrate the presence of coexisting (metastable) phases, when the system is in the proximity of the transition. We measure obser...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2025
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We demonstrate the presence of coexisting (metastable) phases, when the system is in the proximity of the transition. We measure observables such as the free energy, the expectation value of the plaquette operator and of the Polyakov loop, as well as the specific heat, and the Binder cumulant. We use these results to obtain a high-precision measurement of the critical coupling at the confinement-deconfinement transition, and assess its systematic uncertainty, for one value of the lattice extent in the time di- rection. Furthermore, we perform an extensive study of the finite-volume behaviour of the lattice system, by repeating the measurements for fixed lattice time extent, while increasing the spatial size of the lattice. We hence characterise the first-order transition on the lattice, and present the first results in the literature on this theory for the infinite volume extrapolation of lattice quantities related to latent heat and interface tension.Gauge theories with Sp(4) group have been proposed as new dark sectors to provide a funda- mental origin for the current phenomenological evidence of dark matter. A phase transition at high temperature, in such a new dark sector, occurring in the early universe, might have left a relic stochastic background of gravitational waves. Our results represent a milestone toward establishing whether such a new physics signal is detectable in future experiments, as they enter the calculation of the parameters, &#x3B1; and &#x3B2;, controlling the power spectrum of gravitational waves. 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Zierler for useful discussions on future developments of the software used for this work. We also thank Deog Ki Hong, Jong-Wan Lee, and Fabian Zierler for comments on early versions of the manuscript. The work of E.&#x2009;B. has been funded by the UKRI Science and Technologies Facilities Council (STFC) Research Software Engineering Fellowship EP/V052489/1, by the STFC under Consolidated Grant No. ST/X000648/1, and by the ExaTEPP Project No. EP/X017168/1. The work of D.&#x2009;V. is supported by STFC under Consolidated Grant No. ST/X000680/1. The work of D.&#x2009;M. is supported by a studentship awarded by the Data Intensive Centre for Doctoral Training, which is funded by the STFC Grant No. ST/P006779/1. B.&#x2009;L. and M.&#x2009;P. received funding from the European Research Council (ERC) under the European Union&#x2019;s Horizon 2020 research and innovation program under Grant Agreement No. 813942, and by STFC under Consolidated Grants No. ST/P00055X/1, No. ST/T000813/1, and No. ST/X000648/1. The work of B.&#x2009;L. is further supported in part by the Royal Society Wolfson Research Merit Award No. WM170010 and by the Leverhulme Trust Research Fellowship No. RF-2020-4619. Numerical simulations have been performed on the Swansea SUNBIRD cluster (part of the Supercomputing Wales project) and AccelerateAI A100 GPU system. The Swansea SUNBIRD system and AccelerateAI are part funded by the European Regional Development Fund (ERDF) via Welsh Government. Numerical simulations have been performed on the DiRAC Data Intensive service at Leicester. The DiRAC Data Intensive service equipment at Leicester was funded by BEIS capital funding via STFC Capital Grants No. ST/K000373/1 and No. ST/R002363/1 and STFC DiRAC Operations Grant No. ST/R001014/1. Numerical simulations have used the DiRAC Extreme Scaling service at the University of Edinburgh. The DiRAC Data Intensive service at Leicester is operated by the University of Leicester IT Services, and the DiRAC Extreme Scaling service is operated by the Edinburgh Parallel Computing Centre, they form part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This work used the DiRAC Data Intensive service (CSD3) at the University of Cambridge, managed by the University of Cambridge University Information Services on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The DiRAC component of CSD3 at Cambridge was funded by BEIS, UKRI, and STFC capital funding and STFC operations grants. DiRAC is part of the UKRI Digital Research Infrastructure. The DiRAC Extreme Scaling service was funded by BEIS capital funding via STFC Capital Grant No. ST/R00238X/1 and STFC DiRAC Operations Grant No. ST/R001006/1. DiRAC is part of the National e-Infrastructure. This work was supported by the Supercomputer Fugaku Start-up Utilization Program of RIKEN. 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spelling 2025-06-19T12:53:19.6226195 v2 69422 2025-05-06 Density of states method for symplectic gauge theories at finite temperature e1a8e7927d2b093acdc54e74eac95e38 0000-0002-1678-6701 Ed Bennett Ed Bennett true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 341431eb263f8df9a38d8df4ae3d1cb2 David Mason David Mason true false 3ce295f2c7cc318bac7da18f9989d8c3 0000-0002-2251-0111 Maurizio Piai Maurizio Piai true false 2025-05-06 MACS We study the finite-temperature behaviour of the Sp(4) Yang-Mills lattice theory in four di- mensions, by applying the Logarithmic Linear Relaxation (LLR) algorithm. We demonstrate the presence of coexisting (metastable) phases, when the system is in the proximity of the transition. We measure observables such as the free energy, the expectation value of the plaquette operator and of the Polyakov loop, as well as the specific heat, and the Binder cumulant. We use these results to obtain a high-precision measurement of the critical coupling at the confinement-deconfinement transition, and assess its systematic uncertainty, for one value of the lattice extent in the time di- rection. Furthermore, we perform an extensive study of the finite-volume behaviour of the lattice system, by repeating the measurements for fixed lattice time extent, while increasing the spatial size of the lattice. We hence characterise the first-order transition on the lattice, and present the first results in the literature on this theory for the infinite volume extrapolation of lattice quantities related to latent heat and interface tension.Gauge theories with Sp(4) group have been proposed as new dark sectors to provide a funda- mental origin for the current phenomenological evidence of dark matter. A phase transition at high temperature, in such a new dark sector, occurring in the early universe, might have left a relic stochastic background of gravitational waves. Our results represent a milestone toward establishing whether such a new physics signal is detectable in future experiments, as they enter the calculation of the parameters, α and β, controlling the power spectrum of gravitational waves. We also outline the process needed in the continuum extrapolation of our measurements, and test its feasibility on one additional choice of temporal extent of the lattice. Journal Article Physical Review D 111 11 American Physical Society (APS) 2470-0010 2470-0029 16 6 2025 2025-06-16 10.1103/physrevd.111.114511 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Other We would like to thank F. Zierler for useful discussions on future developments of the software used for this work. We also thank Deog Ki Hong, Jong-Wan Lee, and Fabian Zierler for comments on early versions of the manuscript. The work of E. B. has been funded by the UKRI Science and Technologies Facilities Council (STFC) Research Software Engineering Fellowship EP/V052489/1, by the STFC under Consolidated Grant No. ST/X000648/1, and by the ExaTEPP Project No. EP/X017168/1. The work of D. V. is supported by STFC under Consolidated Grant No. ST/X000680/1. The work of D. M. is supported by a studentship awarded by the Data Intensive Centre for Doctoral Training, which is funded by the STFC Grant No. ST/P006779/1. B. L. and M. P. received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 813942, and by STFC under Consolidated Grants No. ST/P00055X/1, No. ST/T000813/1, and No. ST/X000648/1. The work of B. L. is further supported in part by the Royal Society Wolfson Research Merit Award No. WM170010 and by the Leverhulme Trust Research Fellowship No. RF-2020-4619. Numerical simulations have been performed on the Swansea SUNBIRD cluster (part of the Supercomputing Wales project) and AccelerateAI A100 GPU system. The Swansea SUNBIRD system and AccelerateAI are part funded by the European Regional Development Fund (ERDF) via Welsh Government. Numerical simulations have been performed on the DiRAC Data Intensive service at Leicester. The DiRAC Data Intensive service equipment at Leicester was funded by BEIS capital funding via STFC Capital Grants No. ST/K000373/1 and No. ST/R002363/1 and STFC DiRAC Operations Grant No. ST/R001014/1. Numerical simulations have used the DiRAC Extreme Scaling service at the University of Edinburgh. The DiRAC Data Intensive service at Leicester is operated by the University of Leicester IT Services, and the DiRAC Extreme Scaling service is operated by the Edinburgh Parallel Computing Centre, they form part of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This work used the DiRAC Data Intensive service (CSD3) at the University of Cambridge, managed by the University of Cambridge University Information Services on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The DiRAC component of CSD3 at Cambridge was funded by BEIS, UKRI, and STFC capital funding and STFC operations grants. DiRAC is part of the UKRI Digital Research Infrastructure. The DiRAC Extreme Scaling service was funded by BEIS capital funding via STFC Capital Grant No. ST/R00238X/1 and STFC DiRAC Operations Grant No. ST/R001006/1. DiRAC is part of the National e-Infrastructure. This work was supported by the Supercomputer Fugaku Start-up Utilization Program of RIKEN. This work used computational resources of the supercomputer Fugaku provided by RIKEN through the HPCI System Research Project (Project ID: hp230397). 2025-06-19T12:53:19.6226195 2025-05-06T08:59:27.3363632 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Ed Bennett 0000-0002-1678-6701 1 Biagio Lucini 0000-0001-8974-8266 2 David Mason 3 Maurizio Piai 0000-0002-2251-0111 4 Enrico Rinaldi 0000-0003-4134-809x 5 Davide Vadacchino 0000-0002-5783-5602 6 69422__34520__cf07b99b84414774a012401ac6f29cde.pdf 69422.VoR.pdf 2025-06-19T12:48:49.9810926 Output 3352328 application/pdf Version of Record true Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. true eng https://creativecommons.org/licenses/by/4.0/ 321 Ed Bennett 0000-0002-1678-6701 E.J.Bennett@Swansea.ac.uk true https://doi.org/10.5281/zenodo.13807598 false 322 Ed Bennett 0000-0002-1678-6701 E.J.Bennett@Swansea.ac.uk true https://doi.org/10.5281/zenodo.13807993 false
title Density of states method for symplectic gauge theories at finite temperature
spellingShingle Density of states method for symplectic gauge theories at finite temperature
Ed Bennett
Biagio Lucini
David Mason
Maurizio Piai
title_short Density of states method for symplectic gauge theories at finite temperature
title_full Density of states method for symplectic gauge theories at finite temperature
title_fullStr Density of states method for symplectic gauge theories at finite temperature
title_full_unstemmed Density of states method for symplectic gauge theories at finite temperature
title_sort Density of states method for symplectic gauge theories at finite temperature
author_id_str_mv e1a8e7927d2b093acdc54e74eac95e38
7e6fcfe060e07a351090e2a8aba363cf
341431eb263f8df9a38d8df4ae3d1cb2
3ce295f2c7cc318bac7da18f9989d8c3
author_id_fullname_str_mv e1a8e7927d2b093acdc54e74eac95e38_***_Ed Bennett
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
341431eb263f8df9a38d8df4ae3d1cb2_***_David Mason
3ce295f2c7cc318bac7da18f9989d8c3_***_Maurizio Piai
author Ed Bennett
Biagio Lucini
David Mason
Maurizio Piai
author2 Ed Bennett
Biagio Lucini
David Mason
Maurizio Piai
Enrico Rinaldi
Davide Vadacchino
format Journal article
container_title Physical Review D
container_volume 111
container_issue 11
publishDate 2025
institution Swansea University
issn 2470-0010
2470-0029
doi_str_mv 10.1103/physrevd.111.114511
publisher American Physical Society (APS)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description We study the finite-temperature behaviour of the Sp(4) Yang-Mills lattice theory in four di- mensions, by applying the Logarithmic Linear Relaxation (LLR) algorithm. We demonstrate the presence of coexisting (metastable) phases, when the system is in the proximity of the transition. We measure observables such as the free energy, the expectation value of the plaquette operator and of the Polyakov loop, as well as the specific heat, and the Binder cumulant. We use these results to obtain a high-precision measurement of the critical coupling at the confinement-deconfinement transition, and assess its systematic uncertainty, for one value of the lattice extent in the time di- rection. Furthermore, we perform an extensive study of the finite-volume behaviour of the lattice system, by repeating the measurements for fixed lattice time extent, while increasing the spatial size of the lattice. We hence characterise the first-order transition on the lattice, and present the first results in the literature on this theory for the infinite volume extrapolation of lattice quantities related to latent heat and interface tension.Gauge theories with Sp(4) group have been proposed as new dark sectors to provide a funda- mental origin for the current phenomenological evidence of dark matter. A phase transition at high temperature, in such a new dark sector, occurring in the early universe, might have left a relic stochastic background of gravitational waves. Our results represent a milestone toward establishing whether such a new physics signal is detectable in future experiments, as they enter the calculation of the parameters, α and β, controlling the power spectrum of gravitational waves. We also outline the process needed in the continuum extrapolation of our measurements, and test its feasibility on one additional choice of temporal extent of the lattice.
published_date 2025-06-16T05:28:09Z
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score 11.089386

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