The generalized TAP free energy II

Abstract

In a recent paper [14], 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.

arXiv comment28 pages

References in corpus (12)

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• The Parisi formula has a unique minimizer
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• The TAP-Plefka variational principle for the spherical SK model
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Cited by in corpus (6)

• Concentration of the complexity of spherical pure $p$-spin models at arbitrary energies
• Optimizing Mean Field Spin Glasses with External Field
• Dynamics for spherical spin glasses: disorder dependent initial conditions
• On the TAP equations via the cavity approach in the generic mixed $p$-spin models
• Convergence of the free energy for spherical spin glasses
• On the REM approximation of TAP free energies