A neural network study of the phase transitions of the two-dimensional antiferromagnetic $q$-state Potts models on the square lattice

TL;DR

This study demonstrates that an unconventional supervised neural network can effectively identify phase transitions in 2D antiferromagnetic Potts models, outperforming traditional autoencoders and potentially reducing the need for extensive training on new systems.

Contribution

Introduces a novel supervised neural network approach that detects phase transitions without prior physics knowledge, applicable across different systems with minimal retraining.

Findings

Supervised NN correctly identifies critical behavior in q=2,3,4 models.

Unsupervised autoencoders fail to detect the phase transitions.

The method reduces the need for retraining on new systems.

Abstract

The critical phenomena of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ 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 $q$-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.