{"title":"Kramers–Wannier duality and Tutte polynomials","authors":"A. A. Kazakov","doi":"10.1134/S0040577924080051","DOIUrl":null,"url":null,"abstract":"<p> We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers–Wannier duality can be derived from the Tutte duality. Using the “contraction–elimination” relation and the Biggs formalism, we derive the high-temperature expansion and discuss possible methods for generalizing the Kramers–Wannier duality to models on nonplanar graphs. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924080051","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers–Wannier duality can be derived from the Tutte duality. Using the “contraction–elimination” relation and the Biggs formalism, we derive the high-temperature expansion and discuss possible methods for generalizing the Kramers–Wannier duality to models on nonplanar graphs.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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