Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model

The authors describe a method for determining the critical point of a second-order phase transitions using a convolutional neural network based on the Ising model on a square lattice. Data for training were obtained using Metropolis algorithm for different temperatures. The neural network was trained on the data corresponding to the low-temperature phase, that is a ferromagnetic one and high-temperature phase, that is a paramagnetic one, respectively. After training, the neural network analyzed input data from the entire temperature range: from $0.1$ to $5.0$ (in dimensionless units) and determined the Curie temperature $T_c$. The accuracy of the obtained results was estimated relative to the Onsager solution for a flat lattice of Ising spins.