18 January, 2010

Lecture 1: Disordered glassy models: a step beyond mean field

Lecture 2: Glassy disordered systems beyond mean filed: hierarchical models

Abstract

The mean-field description of glasses offers a unifying picture of dynamic and thermodynamic aspects of the supercooled and glass phenomenology. However, typical mean-field pathology are present that need to be cured. In particular metastability  persist indefinitely in mean field and activated processes take an infinite time. In this lecture I will discuss some attempts to introduce a finite interaction range in the mean field picture.

I will discuss disordered models with long but finite range interactions (Kac glass models) and their relation with their corresponding counterpart. I will show how a mean field picture holds locally while long scale  display typical features of finite dimensional systems. I will use Kac glass models to test some recent ideas on Random First Order Transition theory. Two length scales emerge from the analysis, giving a detailed picture of the growth of correlations on approaching the glass transition.