https://doi.org/10.1140/epjb/s10051-022-00453-3
Regular Article - Statistical and Nonlinear Physics
Unsupervised machine learning approaches to the q-state Potts model
1
International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy
2
Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina, PI, Brazil
3
Instituto de Física, Universidade Federal do Rio de Janeiro, Cx.P. 68.528, 21941-972, Rio de Janeiro, RJ, Brazil
Received:
30
March
2022
Accepted:
4
November
2022
Published online:
12
November
2022
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 
, for 
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.
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