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

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

Phys Rev D

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

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: Phys Rev D
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URI: https://cronfa.swan.ac.uk/Record/cronfa71727
first_indexed 2026-04-10T12:25:29Z
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spelling 2026-04-10T13:27:55.1924858 v2 71727 2026-04-10 Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit 3ce295f2c7cc318bac7da18f9989d8c3 0000-0002-2251-0111 Maurizio Piai Maurizio Piai true false e1a8e7927d2b093acdc54e74eac95e38 0000-0002-1678-6701 Ed Bennett Ed Bennett true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 2026-04-10 BGPS 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 Phys Rev D 0 0 0 0001-01-01 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University Not Required 2026-04-10T13:27:55.1924858 2026-04-10T11:59:20.5910257 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Maurizio Piai 0000-0002-2251-0111 1 Ed Bennett 0000-0002-1678-6701 2 Biagio Lucini 0000-0001-8974-8266 3 David Mason 0000-0002-1857-1085 4 Enrico Rinaldi 0000-0003-4134-809X 5 Davide Vadacchino 0000-0002-5783-5602 6 Fabian Zierler 0000-0002-8670-4054 7 71727__36491__bb69f679a9df4b129d6befcd3b91a395.pdf 2509.19009v2.pdf 2026-04-10T13:26:39.2560811 Output 1416210 application/pdf Accepted Manuscript true false 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: towards the continuum limit
spellingShingle Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
Maurizio Piai
Ed Bennett
Biagio Lucini
title_short Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
title_full Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
title_fullStr Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
title_full_unstemmed Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
title_sort Finite-temperature Yang-Mills theories with the density of states method: towards the continuum limit
author_id_str_mv 3ce295f2c7cc318bac7da18f9989d8c3
e1a8e7927d2b093acdc54e74eac95e38
7e6fcfe060e07a351090e2a8aba363cf
author_id_fullname_str_mv 3ce295f2c7cc318bac7da18f9989d8c3_***_Maurizio Piai
e1a8e7927d2b093acdc54e74eac95e38_***_Ed Bennett
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
author Maurizio Piai
Ed Bennett
Biagio Lucini
author2 Maurizio Piai
Ed Bennett
Biagio Lucini
David Mason
Enrico Rinaldi
Davide Vadacchino
Fabian Zierler
format Journal article
container_title Phys Rev D
institution Swansea University
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 0001-01-01T05:52:14Z
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