Bernard Derrida College de France
Renormalization and disorder: a simple toy model
The problem of the depinning transition of a line from a random substrate is one of the simplest problems in the the theory of disordered systems. It has a long history among physicists and mathematicians. Still there are some open questions about the nature of this transition.
After a brief review of our present understanding of the problem, I will discuss a simple tree-like toy model which indicates that, when disorder is relevant, the depinning transition becomes an infinite order transition of the Berezinski-Kosterlitz-Thouless type. I will also try to present some recent developments allowing to understand how the precise nature of the singularity at the transition depends on the distribution of disorder.
Video of the lecture