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The Generalized TAP Free Energy II

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, USA

    Wei-Kuo Chen

  2. Department of Mathematics, University of Toronto, Toronto, Canada

    Dmitry Panchenko

  3. Weizmann Institute, Rehovot, Israel

    Eliran Subag

Authors
  1. Wei-Kuo Chen
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  2. Dmitry Panchenko
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  3. Eliran Subag
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Correspondence to Eliran Subag.

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Communicated by H. Spohn

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W. Chen: Partially supported by NSF grant DMS-17-52184.

D. Panchenko: Partially supported by NSERC.

E. Subag Supported by the Simons Foundation.

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Chen, WK., Panchenko, D. & Subag, E. The Generalized TAP Free Energy II. Commun. Math. Phys. 381, 257–291 (2021). https://doi.org/10.1007/s00220-020-03887-x

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