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Smoothening effect of quenched disorder on polymer depinning transitions | | G. Giacomin
; F. L. Toninelli
; | | Date: |
21 Jun 2005 | | Subject: | Probability; Disordered Systems and Neural Networks | math.PR cond-mat.dis-nn | | Affiliation: | Universite’ de Paris 7, ENS Lyon, UMR--CNRS 5672 | | 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 smoothening effect on the transition. | | Source: | arXiv, math.PR/0506431 | | Services: | Forum | Review | PDF | Favorites | |
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