Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model
The complexity of the study of spin glasses is related to their frustrations, due to which classical Monte Carlo algorithms experience serious difficulties when trying to calculate such systems. The main object of research in this paper is two-dimensional Edwards–Anderson model on a square lattice....
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Peter the Great St.Petersburg Polytechnic University
2022-10-01
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| Series: | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| Subjects: | |
| Online Access: | https://physmath.spbstu.ru/article/2022.58.14/ |
| _version_ | 1811256156840001536 |
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| author | Rybin Alexey Kapitan Dmitrii Nefedev Konstantin Makarov Aleksandr Kapitan Vitalii |
| author_facet | Rybin Alexey Kapitan Dmitrii Nefedev Konstantin Makarov Aleksandr Kapitan Vitalii |
| author_sort | Rybin Alexey |
| collection | DOAJ |
| description | The complexity of the study of spin glasses is related to their frustrations, due to which classical Monte Carlo algorithms experience serious difficulties when trying to calculate such systems. The main object of research in this paper is two-dimensional Edwards–Anderson model on a square lattice. In the paper, we propose an optimized Hybrid Monte Carlo method for calculating the values of thermodynamic averages and ground state energies of the frustrated spin glass model. The validity of the results is confirmed by comparison with numerical simulation with the parallel tempering Monte Carlo method, complete enumeration algorithm and robust machine learning approach – RBM neural network. The proposed algorithm has a number of advantages: possible high parallelization of the algorithm to speed up simulation, calculation accuracy and low resource consumption, which allows to calculate lattices of relatively large size. This algorithm can be applied to calculations of lattices with different geometry and sizes. |
| first_indexed | 2024-04-12T17:36:45Z |
| format | Article |
| id | doaj.art-6cffcbd674ad4dcf90c674b760291fb9 |
| institution | Directory Open Access Journal |
| issn | 2405-7223 |
| language | English |
| last_indexed | 2024-04-12T17:36:45Z |
| publishDate | 2022-10-01 |
| publisher | Peter the Great St.Petersburg Polytechnic University |
| record_format | Article |
| series | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| spelling | doaj.art-6cffcbd674ad4dcf90c674b760291fb92022-12-22T03:22:58ZengPeter the Great St.Petersburg Polytechnic UniversitySt. Petersburg Polytechnical University Journal: Physics and Mathematics2405-72232022-10-01153.110.18721/JPM.153.11420714726Hybrid Monte Carlo algorithm for studying the Edwards-Anderson modelRybin Alexey0https://orcid.org/0000-0002-1055-9217Kapitan Dmitrii1https://orcid.org/0000-0001-9815-1891Nefedev Konstantin2https://orcid.org/0000-0001-7330-5137Makarov Aleksandr3https://orcid.org/0000-0002-7778-8364Kapitan Vitalii4https://orcid.org/0000-0002-5068-8910Far Eastern Federal UniversityFar Eastern Federal UniversityFar Eastern Federal UniversityFar Eastern Federal UniversityFar Eastern Federal UniversityThe complexity of the study of spin glasses is related to their frustrations, due to which classical Monte Carlo algorithms experience serious difficulties when trying to calculate such systems. The main object of research in this paper is two-dimensional Edwards–Anderson model on a square lattice. In the paper, we propose an optimized Hybrid Monte Carlo method for calculating the values of thermodynamic averages and ground state energies of the frustrated spin glass model. The validity of the results is confirmed by comparison with numerical simulation with the parallel tempering Monte Carlo method, complete enumeration algorithm and robust machine learning approach – RBM neural network. The proposed algorithm has a number of advantages: possible high parallelization of the algorithm to speed up simulation, calculation accuracy and low resource consumption, which allows to calculate lattices of relatively large size. This algorithm can be applied to calculations of lattices with different geometry and sizes.https://physmath.spbstu.ru/article/2022.58.14/edwards-anderson modelmonte carlo algorithmground statefrustration |
| spellingShingle | Rybin Alexey Kapitan Dmitrii Nefedev Konstantin Makarov Aleksandr Kapitan Vitalii Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model St. Petersburg Polytechnical University Journal: Physics and Mathematics edwards-anderson model monte carlo algorithm ground state frustration |
| title | Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model |
| title_full | Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model |
| title_fullStr | Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model |
| title_full_unstemmed | Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model |
| title_short | Hybrid Monte Carlo algorithm for studying the Edwards-Anderson model |
| title_sort | hybrid monte carlo algorithm for studying the edwards anderson model |
| topic | edwards-anderson model monte carlo algorithm ground state frustration |
| url | https://physmath.spbstu.ru/article/2022.58.14/ |
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