Validity and limitations of supervised learning for phase transition research

Lecture Notes in Computer Science. 2023. Vol. 14389. P. 314–329.

Diana Sukhoverhova, Chertenkov V., Burovskiy E., Shchur L.

We analyze the Ising model and the Baxter-Wu model in two dimensions using deep learning networks trained to classify paramagnetic (PM) and ferromagnetic (FM) phases. We use the usual Metropolis Monte Carlo algorithm to create uncorrelated snapshots of spin states. The images used as training data are labeled as belonging to the PM state or the FM state using analytically known phase transition temperatures depending on a given set of parameters. 
The main result of the paper is that the widely used technique for extraction of the critical temperature directly from the dependence of the output function is not universal. The value of the output function at the critical temperature really depends on the anisotropy of the model under study, the architecture of the deep network, and some parameters of the deep network application.

Keywords: машинное обучение, Critical temperature, Критическая температура, критические индексы, модель Изинга, phase transitions, фазовые переходы, critical exponents, Baxter-Wu model, модель Бакстера-Ву, Machine Learning, Anisotropic models, Ising model, анизотропные модели