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Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit

Ed Bennett Orcid Logo, Biagio Lucini Orcid Logo, David Mason Orcid Logo, Maurizio Piai Orcid Logo, Enrico Rinaldi Orcid Logo, Davide Vadacchino Orcid Logo, Fabian Zierler, (TELOS collaboration)

Physical Review D, Volume: 113, Issue: 7, Start page: 074519

Swansea University Authors: Ed Bennett Orcid Logo, Biagio Lucini Orcid Logo, Maurizio Piai Orcid Logo, Fabian Zierler

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DOI (Published version): 10.1103/ww6s-xw9z

Abstract

A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa71727
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These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the early stages of evolution of our universe, leaving behind a detectable relic stochastic background of gravitational waves. Lattice field theory studies implementing the density of states method have the potential to provide detailed information about the phase transition, and measure the parameters determining the gravitational-wave power spectrum, by overcoming some of the challenges faced by importance-sampling methods. We assess this potential for a representative choice of Yang-Mills theory with Sp(4) gauge group. We characterize its finite-temperature, first-order phase transition, in the thermodynamic (infinite volume) limit, for two different choices of number of sites in the compact time direction, hence taking the first steps towards the continuum limit extrapolation. We demonstrate the persistence of non-perturbative phenomena associated to the first-order phase transition: coexistence of states, metastability, latent heat, surface tension. We find consistency between several different strategies for the extraction of the volume-dependent critical coupling, hence assessing the size of systematic effects. We also determine the minimum choice of ratio between spatial and time extent of the lattice that allows to identify the contribution of the surface tension to the free energy. 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spelling 2026-05-08T10:39:56.5804803 v2 71727 2026-04-10 Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit e1a8e7927d2b093acdc54e74eac95e38 0000-0002-1678-6701 Ed Bennett Ed Bennett true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 3ce295f2c7cc318bac7da18f9989d8c3 0000-0002-2251-0111 Maurizio Piai Maurizio Piai true false 7eb526fdce1693fc0b79f33e74cc182d Fabian Zierler Fabian Zierler true false 2026-04-10 MACS A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the early stages of evolution of our universe, leaving behind a detectable relic stochastic background of gravitational waves. Lattice field theory studies implementing the density of states method have the potential to provide detailed information about the phase transition, and measure the parameters determining the gravitational-wave power spectrum, by overcoming some of the challenges faced by importance-sampling methods. We assess this potential for a representative choice of Yang-Mills theory with Sp(4) gauge group. We characterize its finite-temperature, first-order phase transition, in the thermodynamic (infinite volume) limit, for two different choices of number of sites in the compact time direction, hence taking the first steps towards the continuum limit extrapolation. We demonstrate the persistence of non-perturbative phenomena associated to the first-order phase transition: coexistence of states, metastability, latent heat, surface tension. We find consistency between several different strategies for the extraction of the volume-dependent critical coupling, hence assessing the size of systematic effects. We also determine the minimum choice of ratio between spatial and time extent of the lattice that allows to identify the contribution of the surface tension to the free energy. We observe that this ratio scales non-trivially with the time extent of the lattice, and comment on the implications for future high-precision numerical studies. Journal Article Physical Review D 113 7 074519 American Physical Society (APS) 2470-0010 2470-0029 24 4 2026 2026-04-24 10.1103/ww6s-xw9z COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Other The work of E. B. and B. L. is supported in part by the EPSRC ExCALIBUR program ExaTEPP (Project No. EP/X017168/1). The work of E. B. has also been supported by the UKRI Science and Technology Facilities Council (STFC) Research Software Engineering Fellowship EP/V052489/1. The work of E. B., B. L., and M. P. has been supported in part by the STFC Consolidated Grant No. ST/X000648/1. The work of B. L. is supported in part by the STFC Consolidator Grant No. ST/X00063X/1. The work of B. L. and M. P. has been supported in part by the STFC Consolidated Grant No. ST/T000813/1. 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. D. M. has been supported in part by a studentship awarded by the Data Intensive Centre for Doctoral Training, funded by the STFC Grant No. ST/P006779/1. D. V. is supported in part by STFC under Consolidated Grant No. ST/X000680/1. F. Z. is supported by the STFC Consolidated Grant No. ST/X000648/1. This work used the DiRAC Data Intensive service (CSD3) at the University of Cambridge, the DiRAC Data Intensive service (DIaL3) at the University of Leicester and the DiRAC Extreme Scaling service (Tursa) at the University of Edinburgh, managed respectively by the University of Cambridge University Information Services, the University of Leicester Research Computing Service and by EPCC on behalf of the STFC DiRAC HPC Facility [213]. The DiRAC service at Cambridge, Leicester, and Edinburgh are funded by BEIS, UKRI and STFC capital funding and STFC operations grants. DiRAC is part of the UKRI Digital Research 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 No. hp230397). Numerical simulations have been performed on the Swansea SUNBIRD cluster (part of the Supercomputing Wales project). The Swansea SUNBIRD system is part funded by the European Regional Development Fund (ERDF) via the Welsh Government. 2026-05-08T10:39:56.5804803 2026-04-10T11:59:20.5910257 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 0000-0002-1857-1085 3 Maurizio Piai 0000-0002-2251-0111 4 Enrico Rinaldi 0000-0003-4134-809x 5 Davide Vadacchino 0000-0002-5783-5602 6 Fabian Zierler 7 (TELOS collaboration) 8 71727__36595__17260fffbedc49fb8d53bb39cf44c114.pdf ww6s-xw9z.pdf 2026-04-25T00:11:27.9399035 Output 3150704 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/ 355 Ed Bennett 0000-0002-1678-6701 e.j.bennett@swansea.ac.uk true 10.5281/zenodo.19449913 false 356 Ed Bennett 0000-0002-1678-6701 e.j.bennett@swansea.ac.uk true 10.5281/zenodo.19449799 false
title Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
spellingShingle Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
Ed Bennett
Biagio Lucini
Maurizio Piai
Fabian Zierler
title_short Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
title_full Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
title_fullStr Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
title_full_unstemmed Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
title_sort Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit
author_id_str_mv e1a8e7927d2b093acdc54e74eac95e38
7e6fcfe060e07a351090e2a8aba363cf
3ce295f2c7cc318bac7da18f9989d8c3
7eb526fdce1693fc0b79f33e74cc182d
author_id_fullname_str_mv e1a8e7927d2b093acdc54e74eac95e38_***_Ed Bennett
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
3ce295f2c7cc318bac7da18f9989d8c3_***_Maurizio Piai
7eb526fdce1693fc0b79f33e74cc182d_***_Fabian Zierler
author Ed Bennett
Biagio Lucini
Maurizio Piai
Fabian Zierler
author2 Ed Bennett
Biagio Lucini
David Mason
Maurizio Piai
Enrico Rinaldi
Davide Vadacchino
Fabian Zierler
(TELOS collaboration)
format Journal article
container_title Physical Review D
container_volume 113
container_issue 7
container_start_page 074519
publishDate 2026
institution Swansea University
issn 2470-0010
2470-0029
doi_str_mv 10.1103/ww6s-xw9z
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 A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the early stages of evolution of our universe, leaving behind a detectable relic stochastic background of gravitational waves. Lattice field theory studies implementing the density of states method have the potential to provide detailed information about the phase transition, and measure the parameters determining the gravitational-wave power spectrum, by overcoming some of the challenges faced by importance-sampling methods. We assess this potential for a representative choice of Yang-Mills theory with Sp(4) gauge group. We characterize its finite-temperature, first-order phase transition, in the thermodynamic (infinite volume) limit, for two different choices of number of sites in the compact time direction, hence taking the first steps towards the continuum limit extrapolation. We demonstrate the persistence of non-perturbative phenomena associated to the first-order phase transition: coexistence of states, metastability, latent heat, surface tension. We find consistency between several different strategies for the extraction of the volume-dependent critical coupling, hence assessing the size of systematic effects. We also determine the minimum choice of ratio between spatial and time extent of the lattice that allows to identify the contribution of the surface tension to the free energy. We observe that this ratio scales non-trivially with the time extent of the lattice, and comment on the implications for future high-precision numerical studies.
published_date 2026-04-24T06:24:42Z
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