https://doi.org/10.1140/epjb/s10051-025-01105-y
Topical Review - Statistical and Nonlinear Physics
Artificial intelligence and machine learning for phases and transitions in the Ising model: an overview
Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, 560012, Bangalore, Karnataka, India
Received:
18
August
2025
Accepted:
1
December
2025
Published online:
22
December
2025
The Ising spin model has long been the foundational model for studying phase transitions in theoretical statistical physics. In the wake of the explosion of machine-learning (ML) techniques in recent years, the Ising model has been used for ML applications to phase transitions. In this overview, we discuss the applications of ML, via both supervised and unsupervised learning, to the study of phases and transitions in the Ising model. We also discuss transfer learning and provide some examples of its use for neural networks trained on Ising model spin configurations. We conclude with a summary and some future directions.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
