{"title":"Villain Action in Lattice Gauge Theory","authors":"Ilya Chevyrev, Christophe Garban","doi":"10.1007/s10955-025-03420-1","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that Villain interaction applied to lattice gauge theory can be obtained as the limit of both Wilson and Manton interactions on a larger graph which we call the <i>carpet graph</i>. This is the lattice gauge theory analog of a well-known property for spin <i>O</i>(<i>N</i>) models where Villain type interactions are the limit of <span>\\(\\mathbb {S}^{N-1}\\)</span> spin systems defined on a <i>cable graph</i>. Perhaps surprisingly in the setting of lattice gauge theory, our proof also applies to non-Abelian lattice theory such as <i>SU</i>(3)-lattice gauge theory and its limiting Villain interaction. In the particular case of an Abelian lattice gauge theory, this allows us to extend the validity of Ginibre inequality to the case of the Villain interaction.\n</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03420-1.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-025-03420-1","RegionNum":3,"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 prove that Villain interaction applied to lattice gauge theory can be obtained as the limit of both Wilson and Manton interactions on a larger graph which we call the carpet graph. This is the lattice gauge theory analog of a well-known property for spin O(N) models where Villain type interactions are the limit of \(\mathbb {S}^{N-1}\) spin systems defined on a cable graph. Perhaps surprisingly in the setting of lattice gauge theory, our proof also applies to non-Abelian lattice theory such as SU(3)-lattice gauge theory and its limiting Villain interaction. In the particular case of an Abelian lattice gauge theory, this allows us to extend the validity of Ginibre inequality to the case of the Villain interaction.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.