THE TWO-DIMENSIONAL CONTINUUM RANDOM FIELD ISING MODEL

• 成果类型: Article
• 署名作者: Bowditch, Adam; Sun, Rongfeng
• 署名单位: National University of Singapore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1536
• 发表日期: 2022
• 页码: 419-454
• 关键词: interfaces; Invariance

摘要

In this paper, we construct the two-dimensional continuum random field Ising model via scaling limits of a random field perturbation of the critical two-dimensional Ising model with diminishing disorder strength. Furthermore, we show that almost surely with respect to the continuum random field given by a white noise, the law of the magnetisation field is singular with respect to that of the two-dimensional continuum pure Ising model constructed by Camia, Garban and Newman.