Neural network evidence of a weakly first order phase transition for the two-dimensional 5-state Potts model

TL;DR

This study employs a universal neural network trained on minimal data to analyze the 2D 5-state Potts model, providing strong evidence that the phase transition is weakly first order, surpassing standard neural network capabilities.

Contribution

Introduces a universal neural network trained on minimal data to effectively study phase transitions in large systems, revealing the weakly first order nature of the 2D 5-state Potts model.

Findings

Neural network indicates a weakly first order phase transition.

Results obtained for systems with over 4 million spins.

Method outperforms standard neural networks in this context.

Abstract

A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.