Exploration of phase behavior of classical spin systems using machine learning

Wenjian Hu, Rajiv R. P. Singh, Richard T. Scalettar

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models-the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional XY model-and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (XY model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.

Elguja Archemashvili

Ce Wang, Hui Zhai

Alina A. Chubarova, Ivan A. Mamonov, Marina V. Mamonova +2 more

Computational models adequately representing phase transitions and evaluating the critical system parameters are essential for the understanding of the properties of a wide range of materials. Here we propose a machine learning (ML)-based approach to the identification of the critical point in anisotropic spin systems. Our approach implies training of a convolutional neural network (CNN) model from the correlation matrices obtained by Monte Carlo simulations. Next, the pretrained model is employed as a fast estimator of the critical temperature, which can be extracted in several complementary ways from the CNN model inference, this way improving the robustness of the analysis. The ML-based estimates obtained in this study are in very good agreement with the reference Monte Carlo simulation results, while computational costs are about 10x lower compared to the classical thermodynamic approach.

Jincheng Zhang

Quantum adaptive topology is a novel approach to machine learning that leverages the unique properties of quantum systems to construct models capable of enhanced prediction and control. This paper explores the potential of this technique, focusing on its ability to dynamically adjust topological structures within a machine learning framework. We detail the core mechanisms, argue for the potential advantages, and present a preliminary exploration of its implementation within a specific application – predicting the behavior of complex systems. The paper concludes with a discussion of future research directions and the potential impact of this approach on the field of machine learning.

Yutaka Akagi, Nobuyuki Yoshioka, Hosho Katsura