Supervised and Transfer Learning for Phase Transition Research

Lecture Notes in Computer Science. 2025. Vol. 15406. P. 434–449.

Chertenkov V., Shchur L.

Machine learning is a new tool for investigating physical models. One possible applications is the study of phase transitions analyzing the distribution of spins on regular lattices using supervised learning approach. A new question is the applicability of transfer learning, a network supervised on a particular model and used to infer information about another model.

The input data is simulated using Monte Carlo algorithms, and the spin distribution and correlator distribution are used for training, validation and testing. A fully connected neural network (FCNN), convolutional neural network (CNN) and residual neural network (ResNet) are used for supervised learning. Three two-dimensional spin models – the Ising model, the 4-state Potts model, and the Baxter-Wu model are used to estimate the critical temperature of phase transition and correlation length exponents.

The main conclusion is that transfer learning depends on the model universality class using both spin and correlator distributions and is therefore not robust.

Keywords: Critical temperature, Критическая температура, критические индексы, модель Изинга, critical exponents, transfer learning, Baxter-Wu model, модель Бакстера-Ву, Ising model, deep machine learning, глубокое машинное обучение, перекрестное обучение, 4-state Potts model, 2nd order phase transitions