Prof. Quentin Berger (Universita' Parigi 6)

When: Mercoledi 13 maggio ore 11,

Where: Aula 211, Pal. C Dip. Matematica e Fisica, RomaTre, Largo San L. Murialdo, 1 - 00146 Roma

Title: Disorder relevance for the pinning model (joint work with Hubert Lacoin)

Abstract: A central question in the study of disordered systems (and in particular of their phase transition) is that of disorder relevance: one wants to determine whether an arbitrarily small quantity of disorder affects or not the critical behavior of the system. The physicist Harris provided a simple and general criterion to know whether disorder was relevant or irrelevant for a given d-dimensional system.

In this talk, we will introduce the pinning model, a family of disordered systems, which has attracted much attention in the past decade: it considers a 1-dimensional polymer chain interacting with an inhomogeneous defect line, undergoing a localization phase transition. For this model, Harris' prediction has been rigorously proved, but the marginal case (for which Harris criterion gives no prediction) was partially left open. We will present here a necessary and sufficient condition for disorder relevance for the pinning model, solving completely the question for this model.