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Smoothing Effect of Quenched Disorder on Polymer Depinning Transitions

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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.

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Authors and Affiliations

  1. Laboratoire de Probabilités de P 6 & 7 (CNRS U.M.R. 7599) and Université Paris 7 – Denis Diderot, U.F.R. Mathematiques, Case 7012, 2 place Jussieu, 75251, Paris Cedex 05, France

    Giambattista Giacomin

  2. Laboratoire de Physique, ENS Lyon (CNRS U.M.R. 5672), 46 Allée d’Italie, 69364, Lyon cedex 07, France

    Fabio Lucio Toninelli

Authors
  1. Giambattista Giacomin
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  2. Fabio Lucio Toninelli
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Correspondence to Giambattista Giacomin.

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Communicated by H. Spohn

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Giacomin, G., Toninelli, F.L. Smoothing Effect of Quenched Disorder on Polymer Depinning Transitions. Commun. Math. Phys. 266, 1–16 (2006). https://doi.org/10.1007/s00220-006-0008-2

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  • DOI: https://doi.org/10.1007/s00220-006-0008-2

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