{"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/bulk-property-on-cayley-tree-with-smooth","title":"Bulk Property on Cayley Tree with Smooth Boundary Condition","arxiv_id":"1412.3053","date":"2014-12-09","proceeding":null,"authors":["Hiro-Aki Hotta"],"abstract":"We study a nearest-neighbor hopping model on the Cayley tree under the smooth boundary condition with the modulation function $f_s=\\sin^2[\\pi s/(2M+1)]$, where $s$ is a distance from the central site, and $M$ is the number of shells on the tree. As a result of this smoothing, the particle density in the ground state becomes nearly uniform in the bulk region even when $M$ is relatively small. We compare the calculated particle density at the center with exact result on the Bethe lattice, and they show a good agreement. The calculated bond energy at the center also agrees with that on the Bethe lattice.","url_abs":"http://arxiv.org/abs/1412.3053v1","url_pdf":"http://arxiv.org/pdf/1412.3053v1.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":"bulk-property-on-cayley-tree-with-smooth","repo_url":"https://github.com/h6ak/ssd-cayley-tree","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}