Unsupervised machine learning approaches to the q-state Potts model

被引：6

作者：

Tirelli, Andrea ^{[1
]}

Carvalho, Danyella O. ^{[2
]}

Oliveira, Lucas A. ^{[2
,3
]}

de Lima, Jose P. ^{[2
]}

Costa, Natanael C. ^{[1
,3
]}

dos Santos, Raimundo R. ^{[3
]}

机构：

[1] Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy

[2] Univ Fed Piaui, Dept Fis, BR-64049550 Teresina, PI, Brazil

[3] Univ Fed Rio de Janeiro, Inst Fis, CxP 68-528, BR-21941972 Rio De Janeiro, RJ, Brazil

来源：

EUROPEAN PHYSICAL JOURNAL B | 2022年 / 95卷 / 11期

关键词：

K-means clustering - Learning algorithms - Machine learning - Potts model - Topology;

D O I：

10.1140/epjb/s10051-022-00453-3

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

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-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. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.

引用

页数：12

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