A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models

A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models

The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In...

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Дата:2018
Автори: Richter-Laskowska, M., Khan, H., Trivedi, N., Maśka, M.M.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики конденсованих систем НАН України 2018
Назва видання:Condensed Matter Physics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/157119
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models / M. Richter-Laskowska, H. Khan, N. Trivedi, M.M. Maśka // Condensed Matter Physics. — 2018. — Т. 21, № 3. — С. 33602: 1–11. — Бібліогр.: 32 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1571192019-06-20T01:30:23Z A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models Richter-Laskowska, M. Khan, H. Trivedi, N. Maśka, M.M. The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) the quantum XY model. Перехiд Березинського-Костерлiца-Таулесса є дуже специфiчним фазовим переходом, при якому всi термодинамiчнi величини є неперервними. Тому важко точно визначити критичну температуру. У цiй статтi нами показано, як можна використати нейроннi мережi для розв’язання цього завдання. Зокрема, дослiджено, до якої мiри точнiсть розпiзнавання переходу залежить вiд способу навчання нейронних мереж. Ми застосовуємо наш пiдхiд до трьох рiзних систем: (i) класична XY модель, (ii) фазово-фермiонна модель iз взаємодiєю мiж класичними й квантовими ступенями вiльностi та (iii) квантова XY модель. 2018 Article A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models / M. Richter-Laskowska, H. Khan, N. Trivedi, M.M. Maśka // Condensed Matter Physics. — 2018. — Т. 21, № 3. — С. 33602: 1–11. — Бібліогр.: 32 назв. — англ. 1607-324X PACS: 64.60.-i, 05.70.Fh, 07.05.Mh DOI:10.5488/CMP.21.33602 arXiv:1809.09927 http://dspace.nbuv.gov.ua/handle/123456789/157119 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) the quantum XY model.
format Article
author Richter-Laskowska, M.
Khan, H.
Trivedi, N.
Maśka, M.M.
spellingShingle Richter-Laskowska, M.
Khan, H.
Trivedi, N.
Maśka, M.M.
A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
Condensed Matter Physics
author_facet Richter-Laskowska, M.
Khan, H.
Trivedi, N.
Maśka, M.M.
author_sort Richter-Laskowska, M.
title A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
title_short A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
title_full A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
title_fullStr A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
title_full_unstemmed A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
title_sort machine learning approach to the berezinskii-kosterlitz-thouless transition in classical and quantum models
publisher Інститут фізики конденсованих систем НАН України
publishDate 2018
url http://dspace.nbuv.gov.ua/handle/123456789/157119
citation_txt A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models / M. Richter-Laskowska, H. Khan, N. Trivedi, M.M. Maśka // Condensed Matter Physics. — 2018. — Т. 21, № 3. — С. 33602: 1–11. — Бібліогр.: 32 назв. — англ.
series Condensed Matter Physics
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first_indexed 2023-05-20T17:51:36Z
last_indexed 2023-05-20T17:51:36Z
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