Avalanches, Chaos, and Overlap Locking In Spin Glasses: old problems and recent developments

Perturbations in disordered systems have dramatic effects both in the structure of low energy states that get completely reshuffled and in the aging dynamics that decorrelates from the unperturbed one.  The fragility of the Gibbs states under perturbation and the emergence of a critical Long Range Order are two faces of the same coin. In this talk I will consider the effect of very tiny perturbation and study

(1) the emergence of universal behaviour in the chaotic dependence of disordered Gibbs states in a random field,

(2) the development of strong correlations in weakly coupled systems,

(3) the fluctuations leading to size corrections in the Sherrington-Kirkpatrick model,

(4) The stability of spin-glass RSB states in Dyson-lattice hierarchical spin glasses.

These problems can be addressed in detail at the mean field level through semi-analytical techniques allowing the efficient generation of random trees describing 'infinite volume spin-glass samples'. We get a coherent picture of fluctuations that we submit to test in numerical simulations.