Machine Learning Domain Adaptation in Spin Models with Continuous Phase Transitions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2025. Vol. 112. No. 3. Article 034104.

Chertenkov V., Shchur L.

The main question raised in the  article  is whether a neural network trained on a spin lattice model in one universality class   can be used to test a model in another universality class. The quantities of interest are the critical phase transition temperature and the correlation length exponent. In other words, the question of transfer learning is how ``universal'' the trained network is and under what conditions.
For this purpose, we applied a supervised learning procedure to three two-dimensional models for which critical properties are precisely known: the Ising model, the four-state Potts model, and the Baxter-Wu model. We consider two datasets: one with spins configurations and one with binding energy configurations. We find that estimates of the critical temperature agree well with the known results for both datasets, but not with the results of cross-testing using the energy datasets of the two models: the four-state Potts model and the Ising model.  Estimates of the critical length exponent are less regular, and appear to be more accurate for energy datasets. A good example is the cross-testing using the energy dataset between Ising model and Baxter-Wu model in both training and testing directions. 

Keywords: фазовые переходы, critical exponents, Supervised Machine Learning, transfer learning, models of statistical mechanics, перенос обучения, finite-size analysis, конечно-мерный анализ, 2nd order phase transitions, машинное обучение с учителем, модели статистической механики, критические показатели