@article{ECP1584,
author = {Francesco Caravenna and Martin Borecki},
title = {Localization for $(1+1)$-dimensional pinning models with $(\nabla + \Delta)$-interaction},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {Pinning Model; Polymer Model; Linear Chain Model; Phase Transition; Localization Phenomena; Gradient Interaction; Laplacian Interaction; Free Energy; Markov Chain},
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 $\epsilon \ge 0$. 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 $\epsilon_c = 0$.},
pages = {no. 48, 534-548},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1584},
url = {http://ecp.ejpecp.org/article/view/1584}}