Disordered pinning models and copolymers: beyond annealed bounds

Abstract

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 al. [Europhys. Lett. 8 (1989) 9--13], 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 $0<\alpha <1/2$ 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.

Published in at http://dx.doi.org/10.1214/07-AAP496 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Equality of critical points for polymer depinning transitions with loop exponent one
• Sharp critical behavior for pinning model in random correlated environment
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• Lectures on random polymers
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• A copolymer near a selective interface: variational characterization of the free energy
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• Comments on the Influence of Disorder for Pinning Model in Correlated Gaussian Environment
• Quenched large deviation principle for words in a letter sequence
• Scaling limit of the disordered generalized Poland--Scheraga model for DNA denaturation
• Coarse graining, fractional moments and the critical slope of random copolymers