https://doi.org/10.1140/epjp/s13360-025-06714-1
Regular Article
A Kohonen network approach to phase transition detection
Physics Department, University of Turin, Via Pietro Giuria, 1, 10125, Turin, Italy
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
8
April
2025
Accepted:
1
August
2025
Published online:
16
August
2025
We present a unified, unsupervised approach based on self-organizing maps for the detection and characterization of phase transitions across a variety of classical spin models. By training a 15 × 15 SOM on equilibrium configurations generated via Metropolis sampling, we define a “neural activity” metric R(T) as the fraction of neurons that respond to at least one input at temperature T. Scanning R(T) over a broad temperature range for the Ising, Blume–Capel, Potts, Heisenberg and XY models, we recover both continuous and discontinuous transitions as pronounced peaks or jumps in neural activity. We further demonstrate the robustness of R(T) under additive and flip-type noise, and extend the methodology to non-equilibrium quench dynamics by monitoring R(t) following an instantaneous cooling of the 2D Ising lattice. In all cases, SOM activity faithfully signals critical behavior and topological changes without requiring prior knowledge of the order parameter.
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 Società Italiana di Fisica 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.
