Silvio Franz — University of Salento Lecce #
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 by small perturbations.  This leads to chaotic dependence of the Gibbs state and aging reinitialization upon changes in control parameters. This  fragility of the Gibbs states is strongly related to the emergence of critical Long Range Order of Spin Glass type.  When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when 1 ~ ∆H ≪ N , being ∆H the coupling Hamiltonian and N the system size. 
In this talk I will consider the effect of very tiny perturbations in disordered systems and study
(1) the formation of strong correlations in weakly coupled systems,
(2) the fluctuations leading to size corrections in the Sherrington-Kirkpatrick model,
(3) The stability of spin-glass RSB states in Dyson-lattice hierarchical spin glasses.