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Machine Learning as a universal tool for quantitative investigations of phase transitions

Cinzia Giannetti Orcid Logo, Biagio Lucini Orcid Logo, Davide Vadacchino

Nuclear Physics B, Volume: 944, Start page: 114639

Swansea University Authors: Cinzia Giannetti Orcid Logo, Biagio Lucini Orcid Logo

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DOI (Published version): 10.1016/j.nuclphysb.2019.114639

Abstract

The problem of identifying the phase of a given system for a certain value of the temperature can be reformulated as a classification problem in Machine Learning. Taking as a prototype the Ising model and using the Support Vector Machine as a tool to classify Monte Carlo generated configurations, we...

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Published in: Nuclear Physics B
ISSN: 0550-3213
Published: Elsevier BV 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa50366
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first_indexed 2019-05-15T16:26:37Z
last_indexed 2023-01-11T14:26:48Z
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spelling 2022-09-27T17:22:16.7083094 v2 50366 2019-05-14 Machine Learning as a universal tool for quantitative investigations of phase transitions a8d947a38cb58a8d2dfe6f50cb7eb1c6 0000-0003-0339-5872 Cinzia Giannetti Cinzia Giannetti true false 7e6fcfe060e07a351090e2a8aba363cf 0000-0001-8974-8266 Biagio Lucini Biagio Lucini true false 2019-05-14 MECH The problem of identifying the phase of a given system for a certain value of the temperature can be reformulated as a classification problem in Machine Learning. Taking as a prototype the Ising model and using the Support Vector Machine as a tool to classify Monte Carlo generated configurations, we show that the critical region of the system can be clearly identified and the symmetry that drives the transition can be reconstructed from the performance of the learning process. The role of the discrete symmetry of the system in obtaining this result is discussed. A finite size analysis of the learned Support Vector Machine decision function allows us to determine the critical temperature and critical exponents with a precision that is comparable to that of the most efficient numerical approaches relying on a known Hamiltonian description of the system. For the determination of the critical temperature and of the critical exponent connected with the divergence of the correlation length, other than the availability of a range of temperatures having information on both phases, the method we propose does not rest on any physical input on the system, and in particular is agnostic to its Hamiltonian, its symmetry properties and its order parameter. Hence, our investigation provides a first significant step in the direction of devising robust tools for quantitative analyses of phase transitions in cases in which an order parameter is not known. Journal Article Nuclear Physics B 944 114639 Elsevier BV 0550-3213 Statistical Mechanics, Machine Learning, Phase Transitions, Ising Model 1 7 2019 2019-07-01 10.1016/j.nuclphysb.2019.114639 COLLEGE NANME Mechanical Engineering COLLEGE CODE MECH Swansea University SCOAP3, RCUK, Royal Society, Institution, INFN 2022-09-27T17:22:16.7083094 2019-05-14T11:27:42.0210716 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Cinzia Giannetti 0000-0003-0339-5872 1 Biagio Lucini 0000-0001-8974-8266 2 Davide Vadacchino 3 0050366-04062019154550.pdf 1-s2.0-S0550321319301257-main.pdf 2019-06-04T15:45:50.8370000 Output 1043987 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY). true eng https://creativecommons.org/licenses/by/4.0/
title Machine Learning as a universal tool for quantitative investigations of phase transitions
spellingShingle Machine Learning as a universal tool for quantitative investigations of phase transitions
Cinzia Giannetti
Biagio Lucini
title_short Machine Learning as a universal tool for quantitative investigations of phase transitions
title_full Machine Learning as a universal tool for quantitative investigations of phase transitions
title_fullStr Machine Learning as a universal tool for quantitative investigations of phase transitions
title_full_unstemmed Machine Learning as a universal tool for quantitative investigations of phase transitions
title_sort Machine Learning as a universal tool for quantitative investigations of phase transitions
author_id_str_mv a8d947a38cb58a8d2dfe6f50cb7eb1c6
7e6fcfe060e07a351090e2a8aba363cf
author_id_fullname_str_mv a8d947a38cb58a8d2dfe6f50cb7eb1c6_***_Cinzia Giannetti
7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini
author Cinzia Giannetti
Biagio Lucini
author2 Cinzia Giannetti
Biagio Lucini
Davide Vadacchino
format Journal article
container_title Nuclear Physics B
container_volume 944
container_start_page 114639
publishDate 2019
institution Swansea University
issn 0550-3213
doi_str_mv 10.1016/j.nuclphysb.2019.114639
publisher Elsevier BV
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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
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description The problem of identifying the phase of a given system for a certain value of the temperature can be reformulated as a classification problem in Machine Learning. Taking as a prototype the Ising model and using the Support Vector Machine as a tool to classify Monte Carlo generated configurations, we show that the critical region of the system can be clearly identified and the symmetry that drives the transition can be reconstructed from the performance of the learning process. The role of the discrete symmetry of the system in obtaining this result is discussed. A finite size analysis of the learned Support Vector Machine decision function allows us to determine the critical temperature and critical exponents with a precision that is comparable to that of the most efficient numerical approaches relying on a known Hamiltonian description of the system. For the determination of the critical temperature and of the critical exponent connected with the divergence of the correlation length, other than the availability of a range of temperatures having information on both phases, the method we propose does not rest on any physical input on the system, and in particular is agnostic to its Hamiltonian, its symmetry properties and its order parameter. Hence, our investigation provides a first significant step in the direction of devising robust tools for quantitative analyses of phase transitions in cases in which an order parameter is not known.
published_date 2019-07-01T04:01:47Z
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