Influence of disorder for different pinning models
Abstract
The goal of this talk is to give an overview of the question of disorder relevance for physical systems, through the example of pinning models.
The main question is to determine whether an arbitrarily small amount of disorder may change the properties of the system, in which case disorder is said to be relevant.
I will consider in particular two closely related pinning models (pinning on a line of defect vs. pinning on a random walk) for which this question has been studied. In works with Hubert Lacoin (IMPA), we have established some criteria for disorder relevance in both models: somewhat surprisingly, the criteria are slightly different for the two models, which was not anticipated in the physics literature.