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

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