Sharp critical behavior for pinning model in random correlated environment

TL;DR

This paper analyzes how long-range correlated environments affect the phase transition in a random pinning model, revealing sharp critical behavior and delocalization at the transition point.

Contribution

It provides a precise description of the phase transition and critical exponent for a specific correlated environment, contrasting with previous i.i.d. disorder results.

Findings

Sharp phase transition characterization

Critical exponent for free energy determined

Trajectories are fully delocalized at criticality

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.