Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice

Abstract

This paper presents the investigation of convolutional neural network (CNN) prediction successfully recognizing the temperature of the nonequilibrium phase transitions in two-dimensional (2D) Ising spins on a square lattice. The model uses image snapshots of ferromagnetic 2D spin configurations as an input shape to provide the average output predictions. By considering supervised machine learning techniques, we perform Metropolis Monte Carlo (MC) simulations to generate the configurations. In the equilibrium Ising model, the Metropolis algorithm respects detailed balance condition (DBC), while its nonequilibrium version violates DBC. Violating the DBC of the algorithm is characterized by a parameter −8<ε<8. We find the exact result of the transition temperature Tc(ε) in terms of ε. If we set ε=0, the usual single spin-flip algorithm can be restored, and the equilibrium configurations generated with such a set up are used to train our model. For ε≠0, the system attains the nonequilibrium steady states (NESS), and the modified algorithm generates NESS configurations (test dataset). The trained model is successfully tested on the test dataset. Our result shows that CNN can determine Tc(ε≠0) for various ε values, consistent with the exact result.