Hierarchical pinning model: low disorder relevance in the b=s case

2014/08/14 by Julien Sohier, Sohier, Julien
Computer Science · Mathematics · Physics and Astronomy · #37H10 #60K35 #82B44 #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1408.3208

openalex publication_date 2014/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We consider a hierarchical pinning model introduced by B.Derrida, V.Hakim and J.Vannimenus which undergoes a localization/delocalization phase transition. This model depends on two parameters b and s. We show that in the particular case where b=s, the disorder is weakly relevant, in the sense that at any given temperature, the quenched and the annealed critical points coincide. This is in contrast with the case where b ≠ s.

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