A Neural Network Study of the Phase Transitions of the 2D Antiferromagnetic <i>q</i>-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 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.