Sharp critical behavior for pinning model in random correlated environment

Abstract

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the (quenched) free-energy, and proving that at the critical point the trajectories are fully delocalized. These results contrast with what happens both for the pure model (i.e. without disorder) and for the widely studied case of i.i.d. disorder, where the relevance or irrelevance of disorder on the critical properties is decided via the so-called Harris Criterion.

37 pages, 2 figures

References in corpus (12)

• Smoothing effect of quenched disorder on polymer depinning transitions
• Fractional moment bounds and disorder relevance for pinning models
• Marginal relevance of disorder for pinning models
• A replica-coupling approach to disordered pinning models
• Disordered pinning models and copolymers: beyond annealed bounds
• Quenched and Annealed Critical Points in Polymer Pinning Models
• On the irrelevant disorder regime of pinning models
• The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptotics
• Periodic copolymers at selective interfaces: A Large Deviations approach
• Ivy on the ceiling: first-order polymer depinning transitions with quenched disorder
• On quenched and annealed critical curves of random pinning model with finite range correlations
• Disorder relevance for the random walk pinning model in dimension 3

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