Hierarchical pinning model with site disorder: Disorder is marginally relevant

Hubert Lacoin (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study a hierarchical disordered pinning model with site disorder for which, like in the bond disordered case [5, 8], 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 [8] and it takes explicitly advantage of the inhomogeneous character of the Green function of the model.

Mots clés: Critical behavior; Hierarchical pinning models; Diamond lattices; Quenched disorder; Critical behavior.

Domaines: Probabilités [math.PR]

Hubert Lacoin. Hierarchical pinning model with site disorder: Disorder is marginally relevant. 2008. ⟨hal-00356343⟩