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DISORDERED PINNING MODELS AND COPOLYMERS: BEYOND Annealed Bounds (2008)
| Citations: | 32 - 4 self |
BibTeX
@MISC{Toninelli08disorderedpinning,
author = {Fabio Lucio Toninelli},
title = {DISORDERED PINNING MODELS AND COPOLYMERS: BEYOND Annealed Bounds},
year = {2008}
}
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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 T. Garel et al. [16], 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 non-integer moments of the partition function. As an application, we show that for strong disorder the quenched critical point differs from the annealed one, e.g., if the disorder distribution is Gaussian. In particular, for pinning models with loop exponent 0 < α < 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 âreduced wetting model â introduced by T. Bodineau and G. Giacomin [5]: without restrictions on the law of the underlying renewal, the critical point coincides with the corresponding renormalization group prediction.
Keyphrases
disordered pinning model copolymer beyond annealed bound critical point coincides strong disorder disordered copolymer new variational upper bound non-integer moment loop exponent particular case selective interface partition function copolymer model poland-scheraga model theoretical physic literature corresponding renormalization group prediction general model dna denaturation reduced wetting model free energy various dimension renormalization group argument disorder distribution quenched critical point differs
