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Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

Nicholas Sale Orcid Logo, Jeffrey Giansiracusa, Biagio Lucini Orcid Logo

Physical Review E, Volume: 105, Issue: 2

Swansea University Authors: Jeffrey Giansiracusa, Biagio Lucini Orcid Logo

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DOI (Published version): 10.1103/physreve.105.024121

Abstract

We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nemati...

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Published in: Physical Review E
ISSN: 2470-0045 2470-0053
Published: American Physical Society (APS) 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa59402
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first_indexed 2022-02-15T02:05:36Z
last_indexed 2023-01-11T14:40:39Z
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spelling 2022-08-17T13:10:59.4296569 v2 59402 2022-02-15 Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology 03c4f93e1b94af60eb0c18c892b0c1d9 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 2022-02-15 FGSEN We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length. Journal Article Physical Review E 105 2 American Physical Society (APS) 2470-0045 2470-0053 14 2 2022 2022-02-14 10.1103/physreve.105.024121 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University N.S. has been supported by a Swansea University Research Excellence Scholarship (SURES). J.G. was supported by EPSRC Grant No. EP/R018472/1. B.L. received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. No 813942. The work of B.L. was further supported in part by the UKRI Science and Technology Facilities Council (STFC) Consolidated Grant No. ST/T000813/1, by the Royal Society Wolfson Research Merit Award No. WM170010, and by the Leverhulme Foundation Research Fellowship RF-2020-4619. 2022-08-17T13:10:59.4296569 2022-02-15T01:57:27.0496640 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Nicholas Sale 0000-0003-2091-6051 1 Jeffrey Giansiracusa 2 Biagio Lucini 0000-0001-8974-8266 3 59402__22381__214c7e42f4aa4af0b034f25d8d7ab3a9.pdf 2109.10960.pdf 2022-02-15T02:07:41.5507210 Output 1153188 application/pdf Accepted Manuscript true true eng
title Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
spellingShingle Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
Jeffrey Giansiracusa
Biagio Lucini
title_short Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
title_full Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
title_fullStr Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
title_full_unstemmed Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
title_sort Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
7e6fcfe060e07a351090e2a8aba363cf
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
author Jeffrey Giansiracusa
Biagio Lucini
author2 Nicholas Sale
Jeffrey Giansiracusa
Biagio Lucini
format Journal article
container_title Physical Review E
container_volume 105
container_issue 2
publishDate 2022
institution Swansea University
issn 2470-0045
2470-0053
doi_str_mv 10.1103/physreve.105.024121
publisher American Physical Society (APS)
college_str Faculty of Science and Engineering
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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 Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.
published_date 2022-02-14T04:16:41Z
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