Neural Network Method for Calculation of the Curie Point of the Two-Dimensional Ising Model

Abstract
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 and analysis were obtained using Monte Carlo simulations. 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 J) and determined the Curie point Tc

Keywords
Ising model, Curie point, Monte Carlo method, Convolutional neural network
Funding
This work was supported by a grant from the President of the Russian Federation for State Support of Leading Scientific Schools of the Russian Federation No. NSh-2559.2022.1.2.
УДК 004.032.26, 536.911

Neural Network Method for Calculation of the Curie Point of the Two-Dimensional Ising Model