Unsupervised machine learning approaches to the q-state Potts model

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