Neural network flows of low q-state Potts and clock models

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...

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Vydáno v:New journal of physics Ročník 24; číslo 4; s. 43040 - 43065
Hlavní autoři: Giataganas, Dimitrios, Huang, Ching-Yu, Lin, Feng-Li
Médium: Journal Article
Jazyk:angličtina
Vydáno: Bristol IOP Publishing 01.04.2022
Témata:
autoencoders
Configurations
Critical point
Ising model
Iterative methods
neural network
Neural networks
Physics
q-state Potts model
restricted Boltzmann machine
state Potts model
ISSN:1367-2630, 1367-2630
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Shrnutí: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.
Bibliografie:NJP-114634.R1
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ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ac63da