Kai-Wei Huang | Searcharxiv

arXiv2026

A Machine Learning study of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice

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.

hep-lat↗

arXiv2025

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

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.

hep-lat↗