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

studied thermodynamics of glassy systems like spherical p-spin. below T_c, there are many pure states and partition function decomposed as. Above T_c, unique state (paramagnet).