{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/scaling-behaviour-in-random-non-commutative","title":"Scaling behaviour in random non-commutative geometries","arxiv_id":"1612.00713","date":"2016-12-02","proceeding":null,"authors":["Lisa Glaser"],"abstract":"Random non-commutative geometries are a novel approach to taking a non-perturbative path integral over geometries. They were introduced in arxiv.org/abs/1510.01377, where a first examination was performed. During this examination we found that some geometries show indications of a phase transition. In this article we explore this phase transition further for geometries of type $(1,1)$, $(2,0)$, and $(1,3)$. We determine the pseudo critical points of these geometries and explore how some of the observables scale with the system size. We also undertake first steps towards understanding the critical behaviour through correlations and in determining critical exponents of the system.","url_abs":"http://arxiv.org/abs/1612.00713v2","url_pdf":"http://arxiv.org/pdf/1612.00713v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"scaling-behaviour-in-random-non-commutative","repo_url":"https://github.com/LisaGlaser/MCMCv4","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}