Disorder and critical phenomena: the α=0 copolymer model

• 成果类型: Article
• 署名作者: Berger, Quentin; Giacomin, Giambattista; Lacoin, Hubert
• 署名单位: Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0870-9
• 发表日期: 2019
• 页码: 787-819
• 关键词: quenched disorder; critical-behavior; critical-points; TRANSITION; localization; interface

摘要

The copolymer model is a disordered system built on a discrete renewal process with inter-arrival distribution that decays in a regularly varying fashion with exponent 1+alpha >= 1. It exhibits a localization transition which can be characterized in terms of the free energy of the model: the free energy is zero in the delocalized phase and it is positive in the localized phase. This transition, which is observed when tuning the mean h of the disorder variable, has been tackled in the physics literature notably via a renormalization group procedure that goes under the name of strong disorder renormalization. We focus on the case alpha=0-the critical value hc(beta) of the parameter h is exactly known (for every strength beta of the disorder) in this case-and we provide precise estimates on the critical behavior. Our results confirm the strong disorder renormalization group prediction that the transition is of infinite order, namely that when h SE arrow hc(beta) the free energy vanishes faster than any power of h-hc(beta). But we show that the free energy vanishes much faster than the physicists' prediction.