{"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/a-numerical-study-of-the-zeroes-of-the-grand","title":"A numerical study of the zeros of the grand partition function of $k$-mers on strips of width $k$","arxiv_id":"2409.07744","date":"2024-09-12","proceeding":null,"authors":["Soumyadeep Sarma"],"abstract":"We study numerically, the distribution of the zeros of the grand partition function of $k$-mers on a $k \\times L$ strip in the complex activity (z) plane. Using transfer matrix methods, we find that our results match the analytical predictions of Heilmann and Leib for $k = 2$. However, for $k = 3$, the zeros are confined within a bounded region, suggesting a fundamental difference in critical behavior. This indicates that trimers belong to a distinct universality class in some finite geometries. We observe that the density of zeros along multiple line segments in the complex plane reveals a richer structure than in the dimer case. {Our findings emphasize the role of geometric constraints in shaping the statistical mechanics of $k$-mer models and set the stage for further studies in higher-dimensional lattices.","url_abs":"https://arxiv.org/abs/2409.07744v4","url_pdf":"https://arxiv.org/pdf/2409.07744v4.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":"a-numerical-study-of-the-zeroes-of-the-grand","repo_url":"https://github.com/lo568los/nius-project","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}