2007/09/30 by Fabio Lucio Toninelli · 3 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #math.PR #msc:60K05 #msc:60K35 #msc:82B44
paper · pdf · doi:10.1214/07-aap496
published as Annals of Applied Probability 2008, Vol. 18, No. 4, 1569-1587 · 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)
openalex publication_date 2008/07/21 · arxiv created 2008/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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<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 “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.