T-4

Goal of these problems:

Key concepts:

RSB and the free-entry landscape

We have seen two examples of mean-field models in which the low-T phase is glassy: the REM, and the spherical p-spin. Both these problems are described by a 1-RSB ansatz. The overlap matrix is parametrised by three quantity: the typical overlap $q_{1}^{SP}$ between configurations belonging to the same pure state, the typical overlap $q_{0}^{SP}$ between configurations belonging to different pure states, and the probability $(1-m^{SP})$ that two configurations extracted at equilibrium belong to the same state.