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

TL;DR

This paper explores how various unsupervised machine learning techniques can identify phase transitions in the q-state Potts model, highlighting the effectiveness of non-linear methods like UMAP and TDA in reducing finite size effects.

Contribution

It demonstrates the application of multiple unsupervised learning methods to detect critical temperatures and phase transition types in the Potts model, serving as a benchmark for such approaches.

Findings

All methods successfully identified critical temperatures for q=3,4,5.

Non-linear methods like UMAP and TDA are less affected by finite size effects.

These methods can distinguish between first and second order phase transitions.

Abstract

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.