Deep Machine Learning Investigation of Phase Transitions

P. 397–408.

Chertenkov V., Burovskiy E., Shchur L.

We explore the possibilities of using neural networks to study phase transitions. The main question is the level of accuracy which can be achieved for the estimates of the critical point and critical exponents of statistical physics models. We generate data for two spin models in two dimensions for which analytical solutions exist, the Ising model and Baxter-Wu model, which belong to the different universality classes. We applied six neural networks with three different architectures to the data and estimated the critical temperature and the correlation length exponent. We find that the accuracy of estimation does depend on the neural network architecture. The critical exponents of Baxter-Wu model are estimated by the deep machine learning technique for the first time.

Keywords: модель Изинга, deep learning, Ising model, глубокое обучение, Baxter-Wu model, Finite-size scaling, ResNet, конечномерный анализ, модель Бакстера-Ву

In book

Supercomputing: 8th Russian Supercomputing Days, RuSCDays 2022, Moscow, Russia, September 26–27, 2022, Revised Selected Papers

Vol. 13708. , Springer, 2022.