The Generalized TAP Free Energy II

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 fo...

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Bibliographic Details
Published in:Communications in mathematical physics 2021, Vol.381 (1), p.257-291
Main Authors: Chen, Wei-Kuo, Panchenko, Dmitry, Subag, Eliran
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Free energy
Ising model
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03887-x