Unsupervised machine learning approaches to the $q$-state Potts model

Andrea Tirelli, Danyella O. Carvalho, Lucas A. Oliveira, J. P. Lima, Natanael C. Costa, Raimundo R. dos Santos

Published 2021-12-13, updated 2022-03-18Version 2

In this paper with 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 $T_c(q)$, for $q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are less dependent on finite size effects, while still being able to distinguish between first and second order phase transitions. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.