# The generalized TAP free energy II

## TL;DR

This paper extends the generalized TAP approach for mixed p-spin models, providing a simplified energy representation linked to the Parisi measure and analyzing ground-state configurations at zero temperature.

## Contribution

It introduces a simplified energy representation for TAP states and extends positive temperature results to zero temperature for ground states.

## Key findings

- Energy of TAP states is uniform at a given distance from the origin.
- Ground-state energy and configuration organization are characterized at zero temperature.
- Results connect TAP states with the Parisi measure.

## Abstract

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.