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Machine Learning as a universal tool for quantitative investigations of phase transitions
Nuclear Physics B, Volume: 944, Start page: 114639
Swansea University Authors:
Cinzia Giannetti , Biagio Lucini
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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...
Published in: | Nuclear Physics B |
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ISSN: | 0550-3213 |
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Elsevier BV
2019
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URI: | https://cronfa.swan.ac.uk/Record/cronfa50366 |
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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 |
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a8d947a38cb58a8d2dfe6f50cb7eb1c6 7e6fcfe060e07a351090e2a8aba363cf |
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a8d947a38cb58a8d2dfe6f50cb7eb1c6_***_Cinzia Giannetti 7e6fcfe060e07a351090e2a8aba363cf_***_Biagio Lucini |
author |
Cinzia Giannetti Biagio Lucini |
author2 |
Cinzia Giannetti Biagio Lucini Davide Vadacchino |
format |
Journal article |
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Nuclear Physics B |
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944 |
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114639 |
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2019 |
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Swansea University |
issn |
0550-3213 |
doi_str_mv |
10.1016/j.nuclphysb.2019.114639 |
publisher |
Elsevier BV |
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Faculty of Science and Engineering |
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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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1763753179757936640 |
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11.021648 |