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- W2953002080 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 $delta$-pinning type, with strength $epsilon geq 0$. 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 $epsilon$ must be greater than a strictly positive critical threshold $epsilon_c > 0$. On the other hand, when the self-interaction is purely gradient, it is known that the transition is trivial: an arbitrarily small reward $epsilon > 0$ is sufficient to localize the chain at the defect line ($epsilon_c = 0$). 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 $epsilon_c = 0$." @default.
- W2953002080 created "2019-06-27" @default.
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- W2953002080 date "2010-06-04" @default.
- W2953002080 modified "2023-09-27" @default.
- W2953002080 title "Localization for (1+1)-dimensional pinning models with $(nabla + Delta)$-interaction" @default.
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