FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Neural Network for Prediction of Curie Temperature of Two-Dimensional Ising Model |
Korol A.O., Kapitan V.Yu. |
2021, issue 1, P. 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 |
Download the article (PDF-file) |
References |
| [1] A.M. Turing, “Computing Machinery and Intelligence”, Mind, 59:236 (1950), 433–460. [2] A.G. Makarov i dr., “K chislennomu raschetu frustratsii v modeli Izinga”, Pis'ma v Zhurnal eksperimental'noi i teoreticheskoi fiziki, 110:10 (2019), 700–705. [3] J. Carrasquilla and R.G. Melko, “Machine learning phases of matter”, Nature Physics, 13:5 (2017), 431–434. [4] S. Kenta, et al., “Machine-Learning Studies on Spin Models”, Scientific Reports, 10:1 (2020). [5] K. V. Shapovalova i dr., “Metody kanonicheskogo i mul'tikanonicheskogo semplirovaniia prostranstva sostoianii vektornykh modelei”, Dal'nevostochnyi matematicheskii zhurnal, 17:1 (2017), 124–130. [6] V.Iu. Kapitan i dr., “Termodinamicheskie svoistva sistem spinov Geizenberga na kvadratnoi reshetke s vzaimodeistviem Dzialoshinskogo–Moriia”, Dal'nevostochnyi matematicheskii zhurnal, 20:1 (2020), 63–73. [7] I. Goodfellow, Y. Bengio, A. Courville, Deep learning, MIT press, 2016. [8] M. Abadi, et al., “TensorFlow: Large-scale machine learning on heterogeneous systems”, 2015, TensorFlow. |