Neural Network flows of low q-state Potts and clock Models

TL;DR

This paper demonstrates that neural network flows trained on Monte Carlo configurations of q-state Potts and clock models naturally converge to the critical point, revealing a universal behavior independent of network type.

Contribution

It introduces neural network flows for q-state models, showing they develop stable points at criticality without prior knowledge, suggesting a universal property.

Findings

NN flows converge to the critical point across models

Convergence behavior is independent of NN type and model

Supports connection between NN flows and Renormalization Group

Abstract

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.