T-5

Goal: So far we have discussed the equilibrium properties of disordered systems, that are encoded in their partition function and free energy. In this set of problems, we characterize the energy landscape of a prototypical model, the spherical <math>p${\displaystyle }$-spin.

Key concepts: Langevin dynamics, gradient descent, oout-of-equilibrium dynamics, metastable states, Hessian matrices, random matrix theory.

Metastability and optimisation

- Energy landscapes. Consider p-spin. The function E defines a random energy landscape. The global minimum is the GS. We have seen that we can compute its energy density doing equilibrium