A Neural Network Study of the Phase Transitions of the 2D Antiferromagnetic q-State Potts Models on the Square Lattice
Abstract The critical phenomena of the 2D antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of neural networks (NNs). In particular, an unconventional supervised NN which is trained using no information about the physics of the conside...
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| Vydáno v: | Progress of theoretical and experimental physics Ročník 2025; číslo 3 |
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01.03.2025
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| ISSN: | 2050-3911, 2050-3911 |
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| Abstract | Abstract
The critical phenomena of the 2D antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of neural networks (NNs). In particular, an unconventional supervised NN which is trained using no information about the physics of the considered systems is employed. In addition, conventional unsupervised autoencoders (AECs) are used in our study as well. Remarkably, whereas the conventional AECs either fail or only work partially to uncover the critical phenomena of the systems associated with $q=3$ and $q=4$ investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic $q$-state Potts models. The results obtained in this study suggest convincingly that the applicability of our unconventional supervised NN is broader than one anticipates. In particular, when a new system is studied with our NN, it is likely that it is not necessary to conduct any training, and one only needs to examine whether an appropriate reduced representation of the original raw configurations exists, so that the same already trained NN can be employed to explore the related phase transition efficiently. |
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| AbstractList | Abstract
The critical phenomena of the 2D antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of neural networks (NNs). In particular, an unconventional supervised NN which is trained using no information about the physics of the considered systems is employed. In addition, conventional unsupervised autoencoders (AECs) are used in our study as well. Remarkably, whereas the conventional AECs either fail or only work partially to uncover the critical phenomena of the systems associated with $q=3$ and $q=4$ investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic $q$-state Potts models. The results obtained in this study suggest convincingly that the applicability of our unconventional supervised NN is broader than one anticipates. In particular, when a new system is studied with our NN, it is likely that it is not necessary to conduct any training, and one only needs to examine whether an appropriate reduced representation of the original raw configurations exists, so that the same already trained NN can be employed to explore the related phase transition efficiently. The critical phenomena of the 2D antiferromagnetic \(q\)-state Potts model on the square lattice with \(q=2,3,4\) are investigated using the techniques of neural networks (NNs). In particular, an unconventional supervised NN which is trained using no information about the physics of the considered systems is employed. In addition, conventional unsupervised autoencoders (AECs) are used in our study as well. Remarkably, whereas the conventional AECs either fail or only work partially to uncover the critical phenomena of the systems associated with \(q=3\) and \(q=4\) investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic \(q\)-state Potts models. The results obtained in this study suggest convincingly that the applicability of our unconventional supervised NN is broader than one anticipates. In particular, when a new system is studied with our NN, it is likely that it is not necessary to conduct any training, and one only needs to examine whether an appropriate reduced representation of the original raw configurations exists, so that the same already trained NN can be employed to explore the related phase transition efficiently. |
| Author | Tseng, Yuan-Heng Jiang, Fu-Jiun |
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| Cites_doi | 10.1103/PhysRevB.42.2465 10.1103/PhysRevB.99.121104 10.1103/RevModPhys.91.045002 10.7566/JPSJ.86.063001 10.1103/PhysRevE.99.032142 10.1140/epjp/s13360-023-04741-4 10.1093/ptep/ptac173 10.1088/1367-2630/ab8ab410.1088/1367-2630/ab8ab4 10.1103/RevModPhys.54.235 10.1093/ptep/ptab057 10.1016/j.rinp.2023.107264 10.1103/PhysRevE.97.013306 10.1016/j.rinp.2021.105134 10.1103/PhysRevB.96.195145 10.1023/A:1004599121565 10.1093/ptep/ptad096 10.1038/nphys4035 10.3390/condmat8030083 10.1016/j.physrep.2019.03.001 10.1093/ptep/ptae147 10.7566/JPSJ.85.123706 10.1103/PhysRevLett.63.109 10.1038/nphys4037 10.1140/epjb/e2020-100506-5 10.1016/j.aop.2018.02.018 10.1140/epjp/s13360-024-05563-8 |
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| Snippet | Abstract
The critical phenomena of the 2D antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of... The critical phenomena of the 2D antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of neural... The critical phenomena of the 2D antiferromagnetic \(q\)-state Potts model on the square lattice with \(q=2,3,4\) are investigated using the techniques of... |
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| SubjectTerms | Critical phenomena Neural networks |
| Title | A Neural Network Study of the Phase Transitions of the 2D Antiferromagnetic q-State Potts Models on the Square Lattice |
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