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Title: 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 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 toomore » can be trained to capture phase transitions and critical points.« less

Authors:
 [1];  [2];  [2]
  1. Univ. of California, Davis, CA (United States). Dept. of Physics and Dept. of Computer Science
  2. Univ. of California, Davis, CA (United States). Dept. of Physics
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1368102
Grant/Contract Number:  
NA0002908; DMR-1306048
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 95; Journal Issue: 6; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; phase transitions; data analysis

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. Mon . "Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination". United States. doi:10.1103/PhysRevE.95.062122. https://www.osti.gov/servlets/purl/1368102.
@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 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.},
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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    Constructing neural stationary states for open quantum many-body systems
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