Hierarchical pinning model with site disorder: Disorder is marginally relevant

Details Hierarchical pinning model with site disorder: Disorder is marginally relevant Hierarchical pinning model with site disorder: Disorder is marginally relevant

2008-07-30

arxiv.org/abs/0807.4864v3

Mathematics

Probability

13 pages, 1 figure, final version accepted for publication. to appear in Probability Theory and Related Fields

Scientific paper

We study a hierarchical disordered pinning model with site disorder for which, like in the bond disordered case [6, 9], there exists a value of a parameter b (enters in the definition of the hierarchical lattice) that separates an irrelevant disorder regime and a relevant disorder regime. We show that for such a value of b the critical point of the disordered system is different from the critical point of the annealed version of the model. The proof goes beyond the technique used in [9] and it takes explicitly advantage of the inhomogeneous character of the Green function of the model.

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