On the irrelevant disorder regime of pinning models

Abstract

Recent results have lead to substantial progress in understanding the role of disorder in the (de)localization transition of polymer pinning models. Notably, there is an understanding of the crucial issue of disorder relevance and irrelevance that is now rigorous. In this work, we exploit interpolation and replica coupling methods to obtain sharper results on the irrelevant disorder regime of pinning models. In particular, in this regime, we compute the first order term in the expansion of the free energy close to criticality and this term coincides with the first order of the formal expansion obtained by field theory methods. We also show that the quenched and quenched averaged correlation length exponents coincide, while, in general, they are expected to be different. Interpolation and replica coupling methods in this class of models naturally lead to studying the behavior of the intersection of certain renewal sequences and one of the main tools in this work is precisely renewal theory and the study of these intersection renewals.

arXiv commentPublished in at http://dx.doi.org/10.1214/09-AOP454 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (9)

• Smoothing effect of quenched disorder on polymer depinning transitions
• Marginal relevance of disorder for pinning models
• A replica-coupling approach to disordered pinning models
• Quadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model
• The localized phase of disordered copolymers with adsorption
• There are No Nice Interfaces in 2+1 Dimensional SOS-Models in Random Media
• Critical properties and finite--size estimates for the depinning transition of directed random polymers
• A renewal theory approach to periodic copolymers with adsorption
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder

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• Pinning and wetting transition for (1+1)-dimensional fields with Laplacian interaction
• Hierarchical pinning models, quadratic maps and quenched disorder
• The depinning transition in presence of disorder: a toy model
• Variational characterization of the critical curve for pinning of random polymers
• Equality of critical points for polymer depinning transitions with loop exponent one
• Sharp critical behavior for pinning model in random correlated environment
• Random pinning model with finite range correlations : disorder relevant regime
• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• Localization for a random walk in slowly decreasing random potential