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Unsupervised machine learning approaches to the q-state Potts model

Author

Listed:
  • Andrea Tirelli

    (International School for Advanced Studies (SISSA))

  • Danyella O. Carvalho

    (Universidade Federal do Piauí)

  • Lucas A. Oliveira

    (Universidade Federal do Piauí
    Universidade Federal do Rio de Janeiro)

  • José P. Lima

    (Universidade Federal do Piauí)

  • Natanael C. Costa

    (International School for Advanced Studies (SISSA)
    Universidade Federal do Rio de Janeiro)

  • Raimundo R. Santos

    (Universidade Federal do Rio de Janeiro)

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

Suggested Citation

  • Andrea Tirelli & Danyella O. Carvalho & Lucas A. Oliveira & José P. Lima & Natanael C. Costa & Raimundo R. Santos, 2022. "Unsupervised machine learning approaches to the q-state Potts model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-12, November.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:11:d:10.1140_epjb_s10051-022-00453-3
    DOI: 10.1140/epjb/s10051-022-00453-3
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