A Machine Learning study of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918407261126656 |
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| author | Li, Shang-Wei Huang, Kai-Wei Chen, Chien-Ting Jiang, Fu-Jiun |
| author_facet | Li, Shang-Wei Huang, Kai-Wei Chen, Chien-Ting Jiang, Fu-Jiun |
| contents | The critical phenomena of two-dimensional (2D) antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4,5$ and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN approaches, here we train a multilayer perceptron consisting of only one input layer, one hidden layer, and one output layer with two artificially made stagger-like configurations. Remarkably, despite the fact that the MLP is trained without any input from these considered models, it correctly identifies the critical temperatures of the studied physical systems. Particularly, the MLP outcomes suggest convincingly that the $q=3$ model is critical only at zero temperature and $q=4,5,6$ models remain disordered at all temperatures. Previously, this MLP has been successfully applied to uncover the nature of the phase transitions of 2D antiferromagnetic Ising model with multi-interactions. Therefore, it will be interesting to examine whether the already trained MLP can detect other models with untypical critical phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Machine Learning study of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice Li, Shang-Wei Huang, Kai-Wei Chen, Chien-Ting Jiang, Fu-Jiun High Energy Physics - Lattice Disordered Systems and Neural Networks Statistical Mechanics The critical phenomena of two-dimensional (2D) antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4,5$ and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN approaches, here we train a multilayer perceptron consisting of only one input layer, one hidden layer, and one output layer with two artificially made stagger-like configurations. Remarkably, despite the fact that the MLP is trained without any input from these considered models, it correctly identifies the critical temperatures of the studied physical systems. Particularly, the MLP outcomes suggest convincingly that the $q=3$ model is critical only at zero temperature and $q=4,5,6$ models remain disordered at all temperatures. Previously, this MLP has been successfully applied to uncover the nature of the phase transitions of 2D antiferromagnetic Ising model with multi-interactions. Therefore, it will be interesting to examine whether the already trained MLP can detect other models with untypical critical phenomena. |
| title | A Machine Learning study of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice |
| topic | High Energy Physics - Lattice Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2512.06762 |