Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 381, Issue 1, Pages 257-291Publisher
SPRINGER
DOI: 10.1007/s00220-020-03887-x
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Funding
- NSF [DMS-17-52184]
- NSERC
- Simons Foundation
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In this study, the generalized TAP approach was used for mixed p-spin models with Ising spins at positive and zero temperature, showing that the energy of states at a given distance from the origin is the same. The study also demonstrated analogues of positive temperature results at zero temperature regarding ground-state energy and configurations in space.
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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