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Self-organizing maps as a method for detecting phase transitions and phase identification
ITMO University, Saint-Petersburg, Russian Federation.
ITMO University, Saint-Petersburg, Russian Federation; Science Institute, University of Iceland, Reykjavik, Iceland.
Nordita, Stockholm, Sweden; Department of Physics, KTH Royal Institute of Technology, Stockholm, Sweden.
Department of Physics and Astronomy, Materials Theory Division, Uppsala University, Uppsala, Sweden.
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2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 4, article id 041108Article in journal (Refereed) Published
Abstract [en]

Originating from image recognition, methods of machine learning allow for effective feature extraction and dimensionality reduction in multidimensional datasets, thereby providing an extraordinary tool to deal with classical and quantum models in many-body physics. In this study, we employ a specific unsupervised machine learning technique-self-organizing maps-to create a low-dimensional representation of microscopic states, relevant for macroscopic phase identification and detecting phase transitions. We explore the properties of spin Hamiltonians of two archetype model systems: a two-dimensional Heisenberg ferromagnet and a three-dimensional crystal, Fe in the body-centered-cubic structure. The method of self-organizing maps, which is known to conserve connectivity of the initial dataset, is compared to the cumulant method theory and is shown to be as accurate while being computationally more efficient in determining a phase transition temperature. We argue that the method proposed here can be applied to explore a broad class of second-order phase-transition systems, not only magnetic systems but also, for example, order-disorder transitions in alloys.

Place, publisher, year, edition, pages
American Physical Society, 2019. Vol. 99, no 4, article id 041108
National Category
Materials Engineering Physical Sciences
Identifiers
URN: urn:nbn:se:oru:diva-71885DOI: 10.1103/PhysRevB.99.041108ISI: 000455825600002Scopus ID: 2-s2.0-85059904004OAI: oai:DiVA.org:oru-71885DiVA, id: diva2:1283570
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationSwedish Energy AgencySwedish Foundation for Strategic Research
Note

Funding Agencies:

Russian Science Foundation  17-12-01359 

Horizon2020 RISE project CoExAN 

eSSENCE  

STandUPP 

Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-01-29Bibliographically approved

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Eriksson, Olle

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CiteExportLink to record
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  • apa
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