Geodesic
Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 1, pp. 51-60

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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. 
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     author = {A. O. Korol and V. Yu. Kapitan},
     title = {Neural {Network} for {Prediction} of {Curie} {Temperature} of {Two-Dimensional} {Ising} {Model}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_1_a4/}
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A. O. Korol; V. Yu. Kapitan. Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 1, pp. 51-60. http://geodesic.mathdoc.fr/item/DVMG_2021_21_1_a4/