Skip to main content

Research Repository

Advanced Search

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

Sale, Nicholas; Giansiracusa, Jeffrey; Lucini, Biagio

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology Thumbnail


Authors

Nicholas Sale

Biagio Lucini



Abstract

We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.

Citation

Sale, N., Giansiracusa, J., & Lucini, B. (2022). Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology. Physical Review E, 105(2), https://doi.org/10.1103/physreve.105.024121

Journal Article Type Article
Acceptance Date Feb 1, 2022
Online Publication Date Feb 14, 2022
Publication Date 2022-02
Deposit Date Feb 2, 2022
Publicly Available Date Mar 29, 2024
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 2470-0053
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 105
Issue 2
DOI https://doi.org/10.1103/physreve.105.024121

Files

Accepted Journal Article (934 Kb)
PDF

Copyright Statement
Reprinted with permission from the American Physical Society: Sale, Nicholas, Giansiracusa, Jeffrey & Lucini, Biagio (2022). Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology. Physical Review E 105(2): 024121. © (2022) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.





You might also like



Downloadable Citations