Far Eastern Mathematical Journal

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


Korol A.O., Kapitan V.Yu.

2021, issue 1, Ñ. 51–60
DOI: https://doi.org/10.47910/FEMJ202105


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 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.

Keywords:
Ising model, Curie temperature, Monte Carlo method, Convolutional neural network

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