Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination

Abstract

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-one Ising (BSI) model, and the 2D XY model, and examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow exploration of different phases and symmetry-breaking, but 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 `antoencoder method', and demonstrate that it too can be trained to capture phase transitions and critical points.

14 pages, 14 figures

References in corpus (9)

• Deep Learning in Neural Networks: An Overview
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Learning phase transitions by confusion
• Introduction to astroML: Machine Learning for Astrophysics
• Self-Learning Monte Carlo Method
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Projected Regression Methods for Inverting Fredholm Integrals: Formalism and Application to Analytical Continuation

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• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction
• Machine learning \& artificial intelligence in the quantum domain
• First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited
• Towards meaningful physics from generative models