Random pinning model with finite range correlations : disorder relevant regime

TL;DR

This paper extends results on disorder relevance from i.i.d. to finite range correlated disorder in the random pinning model, confirming the Harris criterion's validity in this more general setting.

Contribution

It demonstrates that the Harris criterion applies to the random pinning model with finite range correlations, expanding previous i.i.d. results.

Findings

Disorder relevance regime identified with differing quenched and annealed critical points.

Harris criterion remains valid with finite range correlations.

Markov renewal techniques are crucial for analysis.

Abstract

The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality of quenched and annealed critical points, as well as exponents, was proved under some conditions on the return exponent of the interarrival times. Here we complete this work by looking at the disorder relevant regime, where annealed and quenched critical points differ. All these results show that the Harris criterion, which was proved to be correct in the i.i.d case, remains valid in our setup. We strongly use Markov renewal constructions that were introduced in the solving of the annealed model.