Journal of Statistical Physics

, Volume 126, Issue 4–5, pp 1025–1044 | Cite as

Critical Properties and Finite-Size Estimates for the Depinning Transition of Directed Random Polymers

  • Fabio Lucio Toninelli


We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in particular, finite-size upper bounds on the order parameter (the contact fraction) in a window around the critical point, shrinking with the system size. Moreover, we derive a new inequality relating the free energy F and an annealed exponent μ which describes extreme fluctuations of the polymer in the localized region. For the particular case of a (1+1)-dimensional interface wetting model, we show that this implies an inequality between the critical exponents which govern the divergence of the disorder-averaged correlation length and of the typical one. Our results are based on the recently proven smoothness property of the depinning transition in presence of quenched disorder and on concentration of measure ideas.


directed polymers pinning and wetting models copolymers depinning transition finite-size estimates concentration of measure typical and average correlation lengths 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Laboratoire de PhysiqueLyon Cedex 07France

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