Minimalist Neural Networks training for phase classification in diluted-Ising models

TL;DR

This paper demonstrates that minimalist neural networks trained on simple configurations can effectively classify phases and determine critical points in complex, unsolved models like the diluted Ising model, outperforming traditional methods.

Contribution

The study introduces a minimalist training approach for neural networks that accurately predicts phase transitions in complex models without extensive data or complex architectures.

Findings

Accurate determination of transition temperatures and percolation densities.

Effective classification of phases in complex, unsolved models.

Potential for simplified neural network training in complex physical systems.

Abstract

In this article, we explore the potential of artificial neural networks, which are trained using an exceptionally simplified catalog of ideal configurations encompassing both order and disorder. We explore the generalisation power of these networks to classify phases in complex models that are far from the simplified training context. As a paradigmatic case, we analyse the order-disorder transition of the diluted Ising model on several two-dimensional crystalline lattices, which does not have an exact solution and presents challenges for most of the available analytical and numerical techniques. Quantitative agreement is obtained in the determination of transition temperatures and percolation densities, with comparatively much more expensive methods. These findings highlight the potential of minimalist training in neural networks to describe complex phenomena and have implications beyond condensed matter physics.