Unsupervised machine learning approaches to the q-state Potts model

Andrea Tirelli (), Danyella O. Carvalho (), Lucas A. Oliveira (), José P. Lima (), Natanael C. Costa () and Raimundo R. Santos ()
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Andrea Tirelli: International School for Advanced Studies (SISSA)
Danyella O. Carvalho: Universidade Federal do Piauí
Lucas A. Oliveira: Universidade Federal do Piauí
José P. Lima: Universidade Federal do Piauí
Natanael C. Costa: International School for Advanced Studies (SISSA)
Raimundo R. Santos: Universidade Federal do Rio de Janeiro

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 11, 1-12

Abstract: 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 $$T_\textrm{c}(q)$$ T c ( q ) , for $$q=3,4$$ 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. Graphical abstract

Date: 2022
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DOI: 10.1140/epjb/s10051-022-00453-3

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