Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder

TL;DR

This paper proves that the presence of disorder in directed polymer models smooths the depinning transition, making it at least second order, which aligns with predictions from the Harris criterion.

Contribution

The paper demonstrates that disorder changes the nature of the depinning transition from first to at least second order in various polymer models.

Findings

Disorder ensures the free energy is differentiable at the critical line.

The contact fraction vanishes continuously at the transition.

Results confirm the Harris criterion predictions.

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.