Machine-Learning Studies on Spin Models

With the recent developments in machine learning, Carrasquilla and Melko have proposed a paradigm that is complementary to the conventional approach for the study of spin models. As an alternative to investigating the thermal average of macroscopic physical quantities, they have used the spin configurations for the classification of the disordered and ordered phases of a phase transition through machine learning. We extend and generalize this method. We focus on the configuration of the long-range correlation function instead of the spin configuration itself, which enables us to provide the same treatment to multi-component systems and the systems with a vector order parameter. We analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition with the same technique to classify three phases: the disordered, the BKT, and the ordered phases. We also present the classification of a model using the training data of a different model.

[1]  Roger G. Melko,et al.  Machine learning phases of matter , 2016, Nature Physics.

[2]  R. B. Potts.  Some generalized order-disorder transformations , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[4]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[5]  Y. Okabe,et al.  Berezinskii–Kosterlitz–Thouless transition on regular and Villain types of q-state clock models , 2019, Journal of Physics A: Mathematical and Theoretical.

[6]  V. L. Berezinskit.  DESTRUCTION OF LONG-RANGE ORDER IN ONE-DIMENSIONAL AND TWO-DIMENSIONAL SYSTEMS POSSESSING A CONTINUOUS SYMMETRY GROUP . II . QUANTUM , 2011 .

[7]  F. Y. Wu.  The Potts model , 1982 .

[8]  J. Kosterlitz,et al.  The critical properties of the two-dimensional xy model , 1974 .

[9]  B. M. Fulk.  MATH , 1992 .

[10]  K. Binder,et al.  A Guide to Monte Carlo Simulations in Statistical Physics: Preface , 2005 .

[11]  Martín Abadi,et al.  TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems , 2016, ArXiv.

[12]  Stefan Wessel,et al.  Parameter diagnostics of phases and phase transition learning by neural networks , 2018, Physical Review B.

[13]  Finite-size scaling of correlation ratio and generalized scheme for the probability-changing cluster algorithm , 2002, cond-mat/0210074.

[14]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[15]  Tzu-Chieh Wei,et al.  Machine learning of phase transitions in the percolation and XY models. , 2018, Physical review. E.

[16]  Roger G. Melko,et al.  Machine learning vortices at the Kosterlitz-Thouless transition , 2017, 1710.09842.

[17]  Weber,et al.  Monte Carlo determination of the critical temperature for the two-dimensional XY model. , 1988, Physical review. B, Condensed matter.

[18]  Joaquin F. Rodriguez-Nieva,et al.  Identifying topological order through unsupervised machine learning , 2018, Nature Physics.

[19]  D. Thouless,et al.  Ordering, metastability and phase transitions in two-dimensional systems , 1973 .

[20]  Naoki Kawashima,et al.  Universal jump in the helicity modulus of the two-dimensional quantum XY model , 1997 .

[21]  V. Berezinsky,et al.  Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems , 1970 .