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arXiv:2511.14081

A Machine Learning study of the two-dimensional antiferromagnetic Ising model with nearest and next-to-nearest interactions on the triangular lattice

Li, Shang-Wei, Tseng, Yuan-Heng, Huang, Kai-Wei, Jiang, Fu-Jiun

Published Nov 18, 2025• 0 citations
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Abstract

We study the phase transitions of the two-dimensional antiferromagnetic Ising model with nearest $J_1$ and next-to-nearest $J_2$ interactions on the triangular lattice for $J_2/J_1 = 0.1, 0.5$ and 1.0. The method of supervised neural networks (NN) is employed for the investigation. While supervised NN is used, no real spin configurations are needed for the training. In addition, two kinds of configurations having their spins be arranged in a staggered pattern are considered as the training set. Remarkably, with this unconventional training strategy, not only the critical temperatures of the studied $J_2/J_1$ are computed accurately by the resulting NN, but also the nature of the investigated phase transitions are determined correctly. Specifically, the phase transitions associated with $J_2/J_1 = 0.1, 0.5$ and 1.0 are first order. These conclusions are consistent with the known results obtained by other methods. Since the training strategy is simple, the NN calculations is highly efficient. It remains to examine whether the unconventional training approach considered in this study can be used to investigate other models with untypical phase transitions or with nontrivial ground state configurations.

DOI
10.48550/arxiv.2511.14081

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We study the phase transitions of the two-dimensional antiferromagnetic Ising model with nearest J1J_1J1​ and next-to-nearest J2J_2J2​ interactions on the triangular lattice for J2/J1=0.1,0.5J_2/J_1 = 0.1, 0.5J2​/J1​=0.1,0.5 and 1.0. The method of supervised neural networks (NN) is employed for the investigation. While supervised NN is used, no real spin configurations are needed for the training. In addition, two kinds of configurations having their spins be arranged in a staggered pattern are considered as the training set. Remarkably, with this unconventional training strategy, not only the critical temperatures of the studied J2/J1J_2/J_1J2​/J1​ are computed accurately by the resulting NN, but also the nature of the investigated phase transitions are determined correctly. Specifically, the phase transitions associated with J2/J1=0.1,0.5J_2/J_1 = 0.1, 0.5J2​/J1​=0.1,0.5 and 1.0 are first order. These conclusions are consistent with the known results obtained by other methods. Since the training strategy is simple, the NN calculations is highly efficient. It remains to examine whether the unconventional training approach considered in this study can be used to investigate other models with untypical phase transitions or with nontrivial ground state configurations.
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Phase transitions of the antiferromagnetic J1J_1J1​-J2J_2J2​-J3J_3J3​ Ising model on the cubic lattice
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A neural network study of the phase transitions of the two-dimensional antiferromagnetic qqq-state Potts models on the square lattice
The critical phenomena of the two-dimensional antiferromagnetic qqq-state Potts model on the square lattice with q=2,3,4q=2,3,4q=2,3,4 are investigated using the techniques of neural networks (NN). 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, while the conventional AECs fail to uncover the critical phenomena of the systems investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic qqq-state 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.
A Machine Learning study of the two-dimensional antiferromagnetic qqq-state Potts model on the square lattice
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