Smoothing effect of quenched disorder on polymer depinning transitions

Abstract

We consider general disordered models of pinning of directed polymers on a defect line. This class contains in particular the $(1+1)$--dimensional interface wetting model, the disordered Poland--Scheraga model of DNA denaturation and other $(1+d)$--dimensional polymers in interaction with flat interfaces. We consider also the case of copolymers with adsorption at a selective interface. Under quite general conditions, these models are known to have a (de)localization transition at some critical line in the phase diagram. In this work we prove in particular that, as soon as disorder is present, the transition is at least of second order, in the sense that the free energy is differentiable at the critical line, so that the order parameter vanishes continuously at the transition. On the other hand, it is known that the corresponding non--disordered models can have a first order (de)localization transition, with a discontinuous first derivative. Our result shows therefore that the presence of the disorder has really a smoothing effect on the transition. The relation with the predictions based on the Harris criterion is discussed.

16 pages, 1 figure. v3: proof of the main theorem simplified, typos corrected, 1 reference added. To appear on Commun. Math. Phys

References in corpus (3)

• Pinning of polymers and interfaces by random potentials
• Estimates on path delocalization for copolymers at selective interfaces
• Numerical study of the disordered Poland-Scheraga model of DNA denaturation

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• Critical properties and finite--size estimates for the depinning transition of directed random polymers
• Copolymers at selective interfaces: new bounds on the phase diagram
• Wetting transition on a one-dimensional disorder
• Ivy on the ceiling: first-order polymer depinning transitions with quenched disorder
• On the localized phase of a copolymer in an emulsion: subcritical percolation regime
• Localization transition in disordered pinning models. Effect of randomness on the critical properties
• On the localized phase of a copolymer in an emulsion: supercritical percolation regime