 Continuous interfaces with disorder: Even strong pinning is too weak in two dimensionsChristof Külske and Enza Orlandi Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 1973-1981 Abstract: We consider statistical mechanics models of continuous height effective interfaces in the presence of a delta pinning of strength [epsilon] at height zero. There is a detailed mathematical understanding of the depinning transition in two dimensions without disorder. Then the variance of the interface height w.r.t. the Gibbs measure stays bounded uniformly in the volume for [epsilon]>0 and diverges like log[epsilon] for [epsilon][downwards arrow]0. How does the presence of a quenched disorder term in the Hamiltonian modify this transition? We show that an arbitrarily weak random field term is enough to beat an arbitrarily strong delta pinning in two dimensions and will cause delocalization. The proof is based on a rigorous lower bound for the overlap between local magnetizations and random fields in finite volume. In two dimensions it implies growth faster than that of the volume which is a contradiction to localization. We also derive a simple complementary inequality which shows that in higher dimensions the fraction of pinned sites converges to one with [epsilon][short up arrow][infinity]. Date: 2008 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:118:y:2008:i:11:p:1973-1981 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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