The Generalized TAP Free Energy II

Wei Kuo Chen, Dmitry Panchenko, Eliran Subag

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 languageEnglish (US)
Pages (from-to)257-291
Number of pages35
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 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.


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