Global exploration of phase behavior in frustrated Ising models using unsupervised learning techniques

We apply a set of machine-learning (ML) techniques for the global exploration of the phase diagrams of two frustrated 2D Ising models with competing interactions. Based on raw Monte Carlo spin configurations generated for random system parameters, we apply principal-component analysis (PCA) and auto-encoders to achieve dimensionality reduction, followed by clustering using the DBSCAN method and a support-vector machine classifier to construct the transition lines between the distinct phases in both models. The results are in very good agreement with available exact solutions, with the auto-encoders leading to quantitatively superior estimates, even for a data set containing only 1400 spin configurations. In addition, the results suggest the existence of a relationship between the structure of the optimized auto-encoder latent space and physical characteristics of both systems. This indicates that the employed approach can be useful in perceiving fundamental properties of physical systems in situations where a priori theoretical insight is unavailable. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

In this study, a set of machine-learning techniques were applied for the global exploration of phase diagrams in frustrated 2D Ising models with competing interactions. By employing dimensionality reduction and clustering methods, transition lines between distinct phases in both models were successfully constructed, yielding results that are in very good agreement with existing exact solutions. Furthermore, the study found a relationship between the structure of the optimized auto-encoder latent space and physical characteristics of the systems.