Abstract
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.