Renewal sequences, disordered potentials, and pinning phenomena

TL;DR

This paper reviews disordered pinning models, highlighting how disorder affects phase transitions and confirming the Harris criterion's predictions through recent results and proof sketches.

Contribution

It provides a comprehensive overview of the state of the art in disordered pinning models, including new insights into disorder effects on critical behavior and phase transitions.

Findings

Disorder influences phase transition nature in pinning models.

Harris criterion accurately predicts disorder effects.

Critical behaviors range from first to infinite order transitions.

Abstract

We give an overview of the state of the art of the analysis of disordered models of pinning on a defect line. This class of models includes a number of well known and much studied systems (like polymer pinning on a defect line, wetting of interfaces on a disordered substrate and the Poland-Scheraga model of DNA denaturation). A remarkable aspect is that, in absence of disorder, all the models in this class are exactly solvable and they display a localization-delocalization transition that one understands in full detail. Moreover the behavior of such systems near criticality is controlled by a parameter and one observes, by tuning the parameter, the full spectrum of critical behaviors, ranging from first order to infinite order transitions. This is therefore an ideal set-up in which to address the question of the effect of disorder on the phase transition,notably on critical properties. We will review recent results that show that the physical prediction that goes under the name of Harris criterion is indeed fully correct for pinning models. Beyond summarizing the results, we will sketch most of the arguments of proof.