THE EFFECTIVE RADIUS OF SELF REPELLING ELASTIC MANIFOLDS
成果类型：
Article
署名作者：
Mueller, Carl; Neuman, Eyal
署名单位：
University of Rochester; Imperial College London
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/23-AAP1956
发表日期：
2023
页码：
5668-5692
关键词：
摘要：
We study elastic manifolds with self-repelling terms and estimate their effective radius. This class of manifolds is modelled by a self-repelling vector-valued Gaussian free field with Neumann boundary conditions over the domain [-N,N](d)boolean AND Z(d), that takes values in R-d. Our main result states that in two dimensions (d=2), the effective radius R-N of the manifold is approximately N. This verifies the conjecture of Kantor, Kardar and Nelson (Phys. Rev. Lett. 58 (1987) 1289-1292) up to a logarithmic correction. Our results in d >= 3 give a similar lower bound on R-N and an upper of order N-d/2. This result implies that self-repelling elastic manifolds undergo a substantial stretching at any dimension.