Abstract
In a recent paper (Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math.), 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 257-291 |
| Number of pages | 35 |
| Journal | Communications in Mathematical Physics |
| Volume | 381 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2021 |
Bibliographical note
Funding Information:E. Subag Supported by the Simons Foundation.
Funding Information:
W. Chen: Partially supported by NSF grant DMS-17-52184.
Funding Information:
D. Panchenko: Partially supported by NSERC.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.