Smoothing effect of quenched disorder on polymer depinning transitions. (English) Zbl 1113.82032

Quenched disorder is expected to smooth phase transitions in many situations. In this work under some conditions on the disorder distribution the authors prove that such effect takes place in models of directed polymers in random media exhibiting a localization/delocalization transition on a defect line. Such a transition may be of first or higher order in the corresponding pure non-disordered cases. It is shown that as soon as disorder is present, the transition is at least of second order. Here the mechanism inducing the smoothing of the transition is based on an estimate of the probability that the polymer visits rare but very favorable regions where the disorder produces a large positive fluctuation of the partition function. Two classes of models are considered: random pinning (or wetting) models and random copolymer at selective interfaces.


82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
82D60 Statistical mechanics of polymers
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