Infinite disorder renormalization fixed point for the continuum random field Ising chain

• 成果类型: Article
• 署名作者: Collin, Orphee; Giacomin, Giambattista; Hu, Yueyun
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01284-2
• 发表日期: 2024
• 页码: 881-939
• 关键词: singular behavior; lyapunov exponent; diffusion; PRODUCTS

摘要

We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently described as a sequence of spin domains with alternating signs (domain-wall structure). We show that for fixed centered external field and as spin-spin couplings become large, the domain-wall structure scales to a disorder dependent limit that coincides with the infinite disorder fixed point process introduced by D. S. Fisher in the context of zero temperature quantum Ising chains. In particular, our results establish a number of predictions that one can find in Fisher et al. (Phys Rev E 64:41, 2001). The infinite disorder fixed point process for centered external field is equivalently described in terms of the process of suitably selected extrema of a Brownian trajectory introduced and studied by Neveu and Pitman (in: S & eacute;minaire de probabilit & eacute;s XXIII. Lecture notes in mathematics, vol 1372, pp 239-247, 1989). This characterization of the infinite disorder fixed point is one of the important ingredients of our analysis.