STAT-MECHLGATDec 13, 2021

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

arXiv:2112.06735v2
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This provides a benchmark for applying unsupervised machine learning to study phase transitions in physics, though it is incremental as it compares existing methods on a known model.

The paper tackled the problem of detecting phase transitions in the q-state Potts model using unsupervised machine learning methods, finding that non-linear techniques like UMAP and TDA correctly identified critical temperatures and distinguished between first and second-order transitions with reduced finite size effects.

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.

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