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

TL;DR

This study uses a neural network to identify critical temperatures in 2D antiferromagnetic Potts models, revealing that certain models are critical only at zero temperature or remain disordered, demonstrating the neural network's effectiveness.

Contribution

The paper introduces a simple multilayer perceptron trained without direct input from the models to accurately detect critical phenomena in 2D antiferromagnetic Potts models.

Findings

The neural network correctly identifies critical temperatures for various q-state models.

The q=3 model is critical only at zero temperature.

Models with q=4,5,6 remain disordered at all temperatures.

Abstract

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.