Compression theory for inhomogeneous systems
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866910714488160256 |
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| author | Gökmen, Doruk Efe Biswas, Sounak Huber, Sebastian D. Ringel, Zohar Flicker, Felix Koch-Janusz, Maciej |
| author_facet | Gökmen, Doruk Efe Biswas, Sounak Huber, Sebastian D. Ringel, Zohar Flicker, Felix Koch-Janusz, Maciej |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11934 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compression theory for inhomogeneous systems Gökmen, Doruk Efe Biswas, Sounak Huber, Sebastian D. Ringel, Zohar Flicker, Felix Koch-Janusz, Maciej Statistical Mechanics Disordered Systems and Neural Networks 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. |
| title | Compression theory for inhomogeneous systems |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2301.11934 |