CRITICAL PARAMETER OF RANDOM LOOP MODEL ON TREES

• 成果类型: Article
• 署名作者: Bjornberg, Jakob E.; Ueltschi, Daniel
• 署名单位: Chalmers University of Technology; University of Gothenburg; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1315
• 发表日期: 2018
• 页码: 2063-2082
• 关键词: cycles

摘要

We give estimates of the critical parameter for random loop models that are related to quantum spin systems. A special case of the model that we consider is the interchange- or random-stirring process. We consider here the model defined on regular trees of large degrees, which are expected to approximate high spatial dimensions. We find a critical parameter that indeed shares similarity with existing numerical results for the cubic lattice. In the case of the interchange process, our results improve on earlier work by Angel and by Hammond, in that we determine the second-order term of the critical parameter.