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Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
Physical Review E, Volume: 105, Issue: 2
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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 nemati...
|Published in:||Physical Review E|
American Physical Society (APS)
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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.
Faculty of Science and Engineering
N.S. has been supported by a Swansea University Research Excellence Scholarship (SURES). J.G. was supported by EPSRC Grant No. EP/R018472/1. B.L. received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. No 813942. The work of B.L. was further supported in part by the UKRI Science and Technology Facilities Council (STFC) Consolidated Grant No. ST/T000813/1,
by the Royal Society Wolfson Research Merit Award No. WM170010, and by the Leverhulme Foundation Research Fellowship RF-2020-4619.