Universality for the pinning model in the weak coupling regime

Abstract

We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent $\alpha \in (1/2,1)$. This corresponds to a regime where disorder is known to be relevant, i.e. to change the critical exponent of the localization transition and to induce a non-trivial shift of the critical point. We show that the free energy and critical curve have an explicit universal asymptotic behavior in the weak coupling regime, depending only on the tail of the return time distribution and not on finer details of the models. This is obtained comparing the partition functions with corresponding continuum quantities, through coarse-graining techniques.

36 pages, 1 figure

References in corpus (3)

• Fractional moment bounds and disorder relevance for pinning models
• Smoothing effect of quenched disorder on polymer depinning transitions
• Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift

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