Machine Learning Domain Adaptation in Spin Models with Continuous Phase Transitions

TL;DR

This paper investigates the transferability of neural networks trained on spin lattice models to different universality classes, focusing on critical temperature and correlation length exponent estimation across models.

Contribution

It demonstrates the extent and limitations of transfer learning in neural networks for critical phenomena in spin models, comparing spin configuration and energy dataset effectiveness.

Findings

Critical temperature estimates align with known values.

Energy datasets yield more accurate critical exponent estimates.

Cross-model transferability varies depending on dataset type.

Abstract

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.12