## 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) |
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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.