Machine learning for percolation utilizing auxiliary Ising variables

TL;DR

This paper introduces an auxiliary Ising mapping method enabling unsupervised machine learning to accurately identify percolation thresholds and classify universality classes across various systems and phase transition types.

Contribution

The paper presents a novel auxiliary Ising mapping approach that improves machine learning applications in percolation and correlated systems, regardless of system dimension or transition order.

Findings

Unsupervised learning accurately locates percolation thresholds.

Auxiliary Ising configurations classify universality with high confidence.

Method applies across different dimensions and transition types.

Abstract

Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of the standard percolation as well as a variety of statistical mechanical systems in correlated percolation representations. We demonstrate that unsupervised machine learning is able to accurately locate the percolation threshold, independent of the spatial dimension of system or the type of phase transition, which can be first order or continuous. Moreover, we show that, by neural network machine learning, auxiliary Ising configurations for different universalities can be classified with high confidence level. Our results indicate that the auxiliary Ising mapping method, despite of it simplicity, can advance the application of machine learning in statistical and condensed-matter physics.