Smoothing of depinning transitions for directed polymers with quenched disorder.
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 nondisordered 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.
Giacomin
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Laboratoire de Probabilités de P 6 & 7 (CNRS UMR 7599) and Université Paris, 7-Denis Diderot, UFR Mathématiques, Case 7012, 2 place Jussieu, 75251 Paris cedex 05, France.
Toninelli
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