TY - JOUR
T1 - Neural network flows of low q-state Potts and clock models
AU - Giataganas, Dimitrios
AU - Huang, Ching Yu
AU - Lin, Feng Li
N1 - Funding Information:
DG would like to thank A Athenodorou, R de Mello Koch and F Diakonos for useful discussions and the Institute of Accelerating Systems and Applications (IASA) in Athens. DG’s work was done while in support by the Hellenic Foundation for Research and Innovation (H.F.R.I.) and the General Secretariat for Research and Technology (GSRT), under Grant Agreement No. 2344. He acknowledges the Ministry of Science and Technology of Taiwan grant 111-2636-M-110-008 for support during article revision. CYH is supported by Taiwan Ministry of Science and Technology through Grant MOST 108-2112-M-029-006-MY3. FLL is supported by Taiwan Ministry of Science and Technology through Grant No. 109-2112-M-003-007-MY3, and he also thanks Han-Shiang Kuo and Chung-Hao Liao for discussions on VAE and the support from NCTS.
Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - It is known that a trained restricted Boltzmann machine (RBM) on the binary Monte Carlo Ising spin configurations, generates a series of iterative reconstructed spin configurations which spontaneously flow and stabilize to the critical point of physical system. Here we construct a variety of neural network (NN) flows using the RBM and (variational) autoencoders, to study the q-state Potts and clock models on the square lattice for q = 2, 3, 4. The NN are trained on Monte Carlo spin configurations at various temperatures. We find that the trained NN flow does develop a stable point that coincides with critical point of the q-state spin models. The behavior of the NN flow is nontrivial and generative, since the training is unsupervised and without any prior knowledge about the critical point and the Hamiltonian of the underlying spin model. Moreover, we find that the convergence of the flow is independent of the types of NNs and spin models, hinting a universal behavior. Our results strengthen the potential applicability of the notion of the NN flow in studying various states of matter and offer additional evidence on the connection with the renormalization group flow.
AB - It is known that a trained restricted Boltzmann machine (RBM) on the binary Monte Carlo Ising spin configurations, generates a series of iterative reconstructed spin configurations which spontaneously flow and stabilize to the critical point of physical system. Here we construct a variety of neural network (NN) flows using the RBM and (variational) autoencoders, to study the q-state Potts and clock models on the square lattice for q = 2, 3, 4. The NN are trained on Monte Carlo spin configurations at various temperatures. We find that the trained NN flow does develop a stable point that coincides with critical point of the q-state spin models. The behavior of the NN flow is nontrivial and generative, since the training is unsupervised and without any prior knowledge about the critical point and the Hamiltonian of the underlying spin model. Moreover, we find that the convergence of the flow is independent of the types of NNs and spin models, hinting a universal behavior. Our results strengthen the potential applicability of the notion of the NN flow in studying various states of matter and offer additional evidence on the connection with the renormalization group flow.
KW - autoencoders
KW - neural network
KW - q-state Potts model
KW - restricted Boltzmann machine
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U2 - 10.1088/1367-2630/ac63da
DO - 10.1088/1367-2630/ac63da
M3 - Article
AN - SCOPUS:85130081148
SN - 1367-2630
VL - 24
JO - New Journal of Physics
JF - New Journal of Physics
IS - 4
M1 - 043040
ER -