A comprehensive neural network study of the non-equilibrium phase transition of the two-dimensional Ising model on the square lattice

Using Monte Carlo simulations (MC) and supervised neural networks (NN), we study the non-equilibrium phase transition of the two-dimensional (2D) Ising model on the square lattice. The non-equilibrium phase transition is induced by the violation of the detailed balance condition in the Metropolis algorithm employed to simulate the model. The considered NN is directly adopted from previous studies. In other words, no training is performed in our study. Remarkably, the outcomes from MC and NN are consistent with each other. In particular, our results suggest that the investigated phase transitions belong to the 2D Ising universality class. We conducted a detailed exploration of how the performance of the conventional convolutional neural network (CNN) is affected by the parameters relevant to the training procedure and the testing sets. We also establish the fact that our NN is much more efficient and stable in estimating the critical points than conventional CNNs typically used in the literature.