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

Understand

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 $b \neq s$.