Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder

Abstract

We consider disordered models of pinning of directed polymers on a defect line, including (1+1)-dimensional interface wetting models, disordered Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional polymers in interaction with columnar defects. We consider also random copolymers at a selective interface. These models are known to have a (de)pinning transition at some critical line in the phase diagram. In this work we prove that, as soon as disorder is present, the transition is at least of second order: the free energy is differentiable at the critical line, and the order parameter (contact fraction) vanishes continuously at the transition. On the other hand, it is known that the corresponding non-disordered models can have a first order (de)pinning transition, with a jump in the order parameter. Our results confirm predictions based on the Harris criterion.

arXiv comment4 pages, 1 figure. Version 2: references added, minor changes made. To appear on Phys. Rev. Lett

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Cited by in corpus (22)

• Marginal relevance of disorder for pinning models
• A replica-coupling approach to disordered pinning models
• Loop Dynamics in DNA Denaturation
• The localized phase of disordered copolymers with adsorption
• The depinning transition in presence of disorder: a toy model
• Theory of force-extension curve for modular proteins and DNA hairpins
• Numerical evidence for relevance of disorder in a Poland-Scheraga DNA denaturation model with self-avoidance: Scaling behavior of average quantities
• Critical properties and finite--size estimates for the depinning transition of directed random polymers
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• DNA denaturation and wetting in the presence of disorder
• Wetting transition on a one-dimensional disorder
• Phase transitions in a mechanical system coupled to Glauber spins
• Lectures on random polymers
• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• Localization transition in disordered pinning models. Effect of randomness on the critical properties
• A general smoothing inequality for disordered polymers
• Results and conjectures on a toy model of depinning
• Random wetting transition on the Cayley tree : a disordered first-order transition with two correlation length exponents
• Numerical study of DNA denaturation with self-avoidance: pseudo-critical temperatures and finite size behaviour
• Localization for a random walk in slowly decreasing random potential
• Copolymer with pinning: variational characterization of the phase diagram
• A copolymer near a selective interface: variational characterization of the free energy