Slow dynamics of glassy systems

TL;DR

This paper introduces modern approaches to studying glassy systems, focusing on solvable mean field models like the Random Energy Model and p-spins, and discusses challenges in extending these results to short-range models.

Contribution

It presents a comprehensive overview of solvable mean field models for glassy systems and highlights the difficulties in generalizing these findings to more realistic short-range models.

Findings

Solution methods for mean field models like REM and p-spins

Insights into the properties of glassy systems from solvable models

Discussion of challenges in extending results to short-range models

Abstract

In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I will show how these models can be solved due their mean field properties. Finally, in the last section, I will discuss the difficulties in the generalization of these findings to short range models.