{"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/real-space-renormalisation-approach-to-the","title":"Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics","arxiv_id":"2404.00660","date":"2024-03-31","proceeding":null,"authors":["Syl Shaw","Rudolf A. Römer"],"abstract":"The real-space renormalisation group method can be applied to the Chalker-Coddington model of the quantum Hall transition to provide a convenient numerical estimation of the localisation critical exponent, $\\nu$. Previous such studies found $\\nu\\sim 2.39$ which falls considerably short of the current best estimates by transfer matrix ($\\nu\\approx 2.593$) and exact-diagonalisation studies ($\\nu=2.58(3)$). By increasing the amount of data $500$ fold we can now measure closer to the critical point and find an improved estimate $\\nu\\approx 2.51$. This deviates only $\\sim 3\\%$ from the previous two values and is already better than the $\\sim 7\\%$ accuracy of the classical small-cell renormalisation approach from which our method is adapted. We also study a previously proposed mixing of the Chalker-Coddington model with a classical scattering model which is meant to provide a route to understanding why experimental estimates give a lower $\\nu\\sim 2.3$. Upon implementing this mixing into our RG unit, we find only further increases to the value of $\\nu$.","url_abs":"https://arxiv.org/abs/2404.00660v1","url_pdf":"https://arxiv.org/pdf/2404.00660v1.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":"real-space-renormalisation-approach-to-the","repo_url":"https://github.com/disqs/ccxd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}