The generalized TAP free energy II

Understand

In a recent paper [14], we developed the generalized TAP approach for mixed $p$-spin models with Ising spins at positive temperature.

• Here we extend these results in two directions.
• We find a simplified representation for the energy of the generalized TAP states in terms of the Parisi measure of the model and, in particular, show that the energy of all states at a given distance from the origin is the same.
• Furthermore, we prove the analogues of the positive temperature results at zero temperature, which concern the ground-state energy and the organization of ground-state configurations in space.