Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination
Abstract
Here, 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 triangularlattice Ising models, the BlumeCapel model, a highly degenerate biquadraticexchange spinone 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 symmetrybreaking, 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 wellstudied 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 groundstate 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 toomore »
 Authors:
 Univ. of California, Davis, CA (United States)
 Publication Date:
 Research Org.:
 The Regents of the University of California, Davis, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1368102
 Grant/Contract Number:
 NA0002908
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review E
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 6; Journal ID: ISSN 24700045
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Hu, Wenjian, Singh, Rajiv R. P., and Scalettar, Richard T. Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination. United States: N. p., 2017.
Web. doi:10.1103/PhysRevE.95.062122.
Hu, Wenjian, Singh, Rajiv R. P., & Scalettar, Richard T. Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination. United States. doi:10.1103/PhysRevE.95.062122.
Hu, Wenjian, Singh, Rajiv R. P., and Scalettar, Richard T. 2017.
"Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination". United States.
doi:10.1103/PhysRevE.95.062122.
@article{osti_1368102,
title = {Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination},
author = {Hu, Wenjian and Singh, Rajiv R. P. and Scalettar, Richard T.},
abstractNote = {Here, 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 triangularlattice Ising models, the BlumeCapel model, a highly degenerate biquadraticexchange spinone 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 symmetrybreaking, 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 wellstudied 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 groundstate 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.},
doi = {10.1103/PhysRevE.95.062122},
journal = {Physical Review E},
number = 6,
volume = 95,
place = {United States},
year = 2017,
month = 6
}
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