Uncomputably complex renormalisation group flows

James D. Watson (), Emilio Onorati and Toby S. Cubitt
Additional contact information
James D. Watson: University College London
Emilio Onorati: University College London
Toby S. Cubitt: University College London

Nature Communications, 2022, vol. 13, issue 1, 1-8

Abstract: Abstract Renormalisation group methods are among the most important techniques for analysing the physics of many-body systems: by iterating a renormalisation group map, which coarse-grains the description of a system and generates a flow in the parameter space, physical properties of interest can be extracted. However, recent work has shown that important physical features, such as the spectral gap and phase diagram, may be impossible to determine, even in principle. Following these insights, we construct a rigorous renormalisation group map for the original undecidable many-body system that appeared in the literature, which reveals a renormalisation group flow so complex that it cannot be predicted. We prove that each step of this map is computable, and that it converges to the correct fixed points, yet the resulting flow is uncomputable. This extreme form of unpredictability for renormalisation group flows had not been shown before and goes beyond the chaotic behaviour seen previously.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/s41467-022-35179-4 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-35179-4

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-022-35179-4

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().