{"title":"具有多体相互作用的经典和量子自旋晶格系统的高温簇扩展","authors":"Tong Xuan Nguyen, Roberto Fernández","doi":"10.1007/s10955-024-03231-w","DOIUrl":null,"url":null,"abstract":"<p>We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of “decoupling parameters”, advocated by Park (J. Stat. Phys. <b>27</b>, 553–576 (1982)), which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a <span>\\(\\beta \\)</span>-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small <span>\\(\\beta \\)</span>. To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams Bissacot et al. (J. Stat. Phys. <b>139</b>, 598–617 (2010)). As an application we show that our lower bound of the radius of <span>\\(\\beta \\)</span>-analyticity is larger than Park’s for quantum systems two-body interactions.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"High-Temperature Cluster Expansion for Classical and Quantum Spin Lattice Systems With Multi-Body Interactions\",\"authors\":\"Tong Xuan Nguyen, Roberto Fernández\",\"doi\":\"10.1007/s10955-024-03231-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of “decoupling parameters”, advocated by Park (J. Stat. Phys. <b>27</b>, 553–576 (1982)), which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a <span>\\\\(\\\\beta \\\\)</span>-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small <span>\\\\(\\\\beta \\\\)</span>. To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams Bissacot et al. (J. Stat. Phys. <b>139</b>, 598–617 (2010)). As an application we show that our lower bound of the radius of <span>\\\\(\\\\beta \\\\)</span>-analyticity is larger than Park’s for quantum systems two-body interactions.</p>\",\"PeriodicalId\":667,\"journal\":{\"name\":\"Journal of Statistical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-01-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10955-024-03231-w\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10955-024-03231-w","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}
High-Temperature Cluster Expansion for Classical and Quantum Spin Lattice Systems With Multi-Body Interactions
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of “decoupling parameters”, advocated by Park (J. Stat. Phys. 27, 553–576 (1982)), which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a \(\beta \)-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small \(\beta \). To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams Bissacot et al. (J. Stat. Phys. 139, 598–617 (2010)). As an application we show that our lower bound of the radius of \(\beta \)-analyticity is larger than Park’s for quantum systems two-body interactions.
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.