Unsupervised machine learning approaches to the q-state Potts model

Abstract

In this paper, we study phase transitions of the q-state Potts model through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), k-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures $$T_\textrm{c}(q)$$ , for $$q=3,4$$ and 5, results show that non-linear methods as UMAP and TDA are less dependent on finite-size effects. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.