Hierarchical pinning model with site disorder: Disorder is marginally relevant

2008/07/30 by Hubert Lacoin, Lacoin, Hubert
Mathematics · Physics and Astronomy · #37H99 #60K37 #82B44 #FOS: Mathematics #Probability (math.PR) #Quantum many-body systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.0807.4864

openalex publication_date 2008/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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