Disordered pinning models and copolymers: Beyond annealed bounds

• 成果类型: Article
• 署名作者: Toninelli, Fabio Lucio
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP496
• 发表日期: 2008
• 页码: 1569-1587
• 关键词: polymer depinning transitions; localization transition; selective interfaces; directed polymers; critical-behavior; denaturation; dna

摘要

We consider a general model of a disordered copolymer with adsorption. This includes, as particular cases, a generalization of the copolymer at a selective interface introduced by Garel et a]. [Europhys. Lett. 8 (1989) 9-131, pinning and wetting models in various dimensions, and the Poland-Scheraga model of DNA denaturation. We prove a new variational upper bound for the free energy via an estimation of noninteger moments of the partition function. As an application, we show that for strong disorder the quenched critical point differs from the annealed one, for example, if the disorder distribution is Gaussian. In particular, for pinning models with loop exponent 0 < oe < 1/2 this implies the existence of a transition from weak to strong disorder. For the copolymer model, under a (restrictive) condition on the law of the underlying renewal, we show that the critical point coincides with the one predicted via renormalization group arguments in the theoretical physics literature. A stronger result holds for a reduced wetting model introduced by Bodineau and Giacomin [J. Statist. Phys. 117 (2004) 801-818]: without restrictions on the law of the underlying renewal, the critical point coincides with the corresponding renormalization group prediction.