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We employ unsupervised machine learning techniques to learn latent parameters which best describe states of the two-dimensional Ising model and the three-dimensional XY model.
LIII.on lines and planes of closest fit to systems of points in space
Karl Pearson · 1901
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Zur Theorie der Phasenumwandlungen II
LD Landau · 1937
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Crystal statistics. i. a two-dimensional model with an order-disorder transition
Lars Onsager · 1944
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The monte carlo method
Nicholas Metropolis and S. Ulam · 1949
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Scaling laws for Ising models near T(c)
L. P. Kadanoff · 1966
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Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic heisenberg models
N. D. Mermin and H. Wagner · 1966
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Existence of long-range order in one and two dimensions
P. C. Hohenberg · 1967
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Resonating valence bonds: A new kind of insulator?
P.W. Anderson · 1973
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The renormalization group: Critical phenomena and the kondo problem
Kenneth G. Wilson · 1975
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Kurt Hornik · 1991
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Autoencoders, minimum description length and helmholtz free energy
Geoffrey E. Hinton and Richard S. Zemel · 1993
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Critical behaviour of the 3d XY-model: a monte carlo study
Aloysius P. Gottlob and Martin Hasenbusch · 1993
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Kernel principal component analysis
Bernhard Scholkopf, Alexander Smola, and Klaus-Robert Müller · 1999
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Predicting crystal structures with data mining of quantum calculations
Stefano Curtarolo, Dane Morgan, Kristin Persson, John Rodgers, and Gerbrand Ceder · 2003
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Quantum Field Theory of Many-Body Systems
Xiao gang Wen · 2004
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Z2topological order and the quantum spin hall effect
C. L. Kane and E. J. Mele · 2005
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Auto-encoding variational bayes
D. P. Kingma and M. Welling · 2013
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Machine learning for many-body physics: The case of the anderson impurity model
Louis-François Arsenault, Alejandro Lopez-Bezanilla, O. Anatole von Lilienfeld, and Andrew J. Millis · 2014
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Building autoencoders in keras, May 2014
Francois Chollet · 2014
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An exact mapping between the variational renormalization group and deep learning
P. Mehta and D. J. Schwab · 2014
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Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces
Zhenwei Li, James R. Kermode, and Alessandro De Vita · 2015
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Structure classification and melting temperature prediction in octet AB solids via machine learning
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