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 Electronic Communications in Probability > Vol. 15(2010) > Paper 48 open journal systems 


Localization for (1+1)-dimensional pinning models with (∇ + Δ)-interaction

Francesco Caravenna, Università degli Studi di Padova
Martin Borecki, TU Berlin


Abstract
We study the localization/delocalization phase transition in a class of directed models for a homogeneous linear chain attracted to a defect line. The self-interaction of the chain is of mixed gradient and Laplacian kind, whereas the attraction to the defect line is of δ-pinning type, with strength ε ≥ 0. It is known that, when the self-interaction is purely Laplacian, such models undergo a non-trivial phase transition: to localize the chain at the defect line, the reward ε must be greater than a strictly positive critical threshold εc > 0. On the other hand, when the self-interaction is purely gradient, it is known that the transition is trivial: an arbitrarily small reward ε > 0 is sufficient to localize the chain at the defect line (εc = 0). In this note we show that in the mixed gradient and Laplacian case, under minimal assumptions on the interaction potentials, the transition is always trivial, that is εc = 0.


Full text: PDF

Pages: 534-548

Published on: November 2, 2010
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Electronic Communications in Probability. ISSN: 1083-589X