{"title":"New renormalization group study of the 3-state Potts model and related statistical models","authors":"José Gaite","doi":"10.1016/j.nuclphysb.2025.116801","DOIUrl":null,"url":null,"abstract":"<div><div>The critical behavior of three-state statistical models invariant under the full symmetry group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale invariance in three-dimensional field theory with <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> symmetry. This scale invariance should appear as a non-trivial fixed point of the renormalization group, which has not been found. Our new search, with the non-perturbative renormalization group, finds such a fixed point, as a bifurcation from the trivial fixed point at the critical space dimension <span><math><mi>d</mi><mo>=</mo><mn>10</mn><mo>/</mo><mn>3</mn></math></span>, which extends continuously to <span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span>. It does not correspond to a second-order phase transition of the 3-state Potts model, but is interesting in its own right. In particular, it shows how the <em>ε</em>-expansion can fail.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1011 ","pages":"Article 116801"},"PeriodicalIF":2.5000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321325000112","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
The critical behavior of three-state statistical models invariant under the full symmetry group and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale invariance in three-dimensional field theory with symmetry. This scale invariance should appear as a non-trivial fixed point of the renormalization group, which has not been found. Our new search, with the non-perturbative renormalization group, finds such a fixed point, as a bifurcation from the trivial fixed point at the critical space dimension , which extends continuously to . It does not correspond to a second-order phase transition of the 3-state Potts model, but is interesting in its own right. In particular, it shows how the ε-expansion can fail.
期刊介绍:
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.