{"title":"20 个顶点模型的虚空形成概率和非局部相关函数表示法","authors":"Pete Rigas","doi":"arxiv-2409.05309","DOIUrl":null,"url":null,"abstract":"We study the emptiness formation probability, along with various\nrepresentations for nonlocal correlation functions, of the 20-vertex model. In\ndoing so, we leverage previous arguments for representations of nonlocal\ncorrelation functions for the 6-vertex model, under domain-wall boundary\nconditions, due to Colomo, Di Giulio, and Pronko, in addition to the\ninhomogeneous, and homogeneous, determinantal representations for the 20-vertex\npartition function due to Di Francesco, also under domain-wall boundary\nconditions. By taking a product of row configuration probabilities, we obtain a\ndesired contour integral representation for nonlocal correlations from a\ndeterminantal representation. Finally, a counterpart of the emptiness formation\nprobability is introduced for the 20-vertex model.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model\",\"authors\":\"Pete Rigas\",\"doi\":\"arxiv-2409.05309\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the emptiness formation probability, along with various\\nrepresentations for nonlocal correlation functions, of the 20-vertex model. In\\ndoing so, we leverage previous arguments for representations of nonlocal\\ncorrelation functions for the 6-vertex model, under domain-wall boundary\\nconditions, due to Colomo, Di Giulio, and Pronko, in addition to the\\ninhomogeneous, and homogeneous, determinantal representations for the 20-vertex\\npartition function due to Di Francesco, also under domain-wall boundary\\nconditions. By taking a product of row configuration probabilities, we obtain a\\ndesired contour integral representation for nonlocal correlations from a\\ndeterminantal representation. Finally, a counterpart of the emptiness formation\\nprobability is introduced for the 20-vertex model.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.05309\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05309","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model
We study the emptiness formation probability, along with various
representations for nonlocal correlation functions, of the 20-vertex model. In
doing so, we leverage previous arguments for representations of nonlocal
correlation functions for the 6-vertex model, under domain-wall boundary
conditions, due to Colomo, Di Giulio, and Pronko, in addition to the
inhomogeneous, and homogeneous, determinantal representations for the 20-vertex
partition function due to Di Francesco, also under domain-wall boundary
conditions. By taking a product of row configuration probabilities, we obtain a
desired contour integral representation for nonlocal correlations from a
determinantal representation. Finally, a counterpart of the emptiness formation
probability is introduced for the 20-vertex model.