Branched polymers and dimensional reduction

• 成果类型: Article
• 署名作者: Brydges, DC; Imbrie, JZ
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.158.1019
• 发表日期: 2003
• 页码: 1019-1039
• 关键词: repulsive-core singularity; yang; UNIVERSALITY; animals

摘要

We establish an exact relation between self-avoiding branched polymers in D + 2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D + 2 = 2,3,4 and show that they are corollaries of our result. We explain the connection (first proposed by Parisi and Sourlas) between branched polymers in D + 2 dimensions and the Yang-Lee edge singularity in D dimensions.