Compression theory for inhomogeneous systems

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on inhomogeneous graphs. However, the lack of translational invariance presents a fundamental challenge to theoretical tools, such as the renormalization group, which were so successful in characterizing the universal physical behaviour in critical phenomena. Here we show that compression theory allows the extraction of relevant degrees of freedom in arbitrary geometries, and the development of efficient numerical tools to build an effective theory from data. We demonstrate our method by applying it to a strongly correlated system on an Ammann-Beenker quasicrystal, where it discovers an exotic critical point with broken conformal symmetry. We also apply it to an antiferromagnetic system on non-bipartite random graphs, where any periodicity is absent.

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Publication Details

Journal
Nature Communications
Published
2024-11-25
DOI
https://doi.org/10.1038/s41467-024-54341-8
Citations
3
Primary Topic
Advanced Mathematical Modeling in Engineering
Type
article
Field-Weighted Citation Impact
1.08

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article

Compression theory for inhomogeneous systems

Felix Flicker, Maciej Koch-Janusz, Sebastian D. Huber, Doruk Efe Gökmen et al.
3 citations
Nature Communications
Advanced Mathematical Modeling in Engineering
1.08
article

Compression theory for inhomogeneous systems

Felix Flicker, Maciej Koch-Janusz, Sebastian D. Huber, Doruk Efe Gökmen, Sounak Biswas, Zohar Ringel
article en
3 citations

Abstract

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on inhomogeneous graphs. However, the lack of translational invariance presents a fundamental challenge to theoretical tools, such as the renormalization group, which were so successful in characterizing the universal physical behaviour in critical phenomena. Here we show that compression theory allows the extraction of relevant degrees of freedom in arbitrary geometries, and the development of efficient numerical tools to build an effective theory from data. We demonstrate our method by applying it to a strongly correlated system on an Ammann-Beenker quasicrystal, where it discovers an exotic critical point with broken conformal symmetry. We also apply it to an antiferromagnetic system on non-bipartite random graphs, where any periodicity is absent.

Nature CommunicationsVol. 15(1)
Chicago Institute for Psychoanalysis (US), Hebrew University of Jerusalem (IL), University of Zurich (CH), University of Würzburg (DE), ETH Zurich (CH), University of Bristol (GB), University of Chicago (US), Hainan Tranquility Hospital (CN), University of Saint Joseph (CN), Instituto de Física Teórica (ES)
National Science Foundation, European Commission, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Israel Science Foundation, Engineering and Physical Sciences Research Council
Openalex Percentile: Top 19%
Advanced Mathematical Modeling in Engineering
1.08
DOIOpen Access PDFOpenAlex
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