The realizable solutions of the TAP equations

Abstract

We show that the only solutions of the TAP equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica symmetric and broken replica symmetric states, when the number of spins $N$ is large. Convergence to this same borderline also happens in quenches from a high temperature initial state to a locally stable state where each spin is parallel to its local field; both are examples of self-organized criticality. At this borderline the band of eigenvalues of the Hessian associated with a solution extends to zero, so the states reached have marginal stability. We have also investigated the factors which determine the free energy difference between a stationary solution corresponding to a saddle point and its associated minimum, which is the barrier which has to be surmounted to escape from the vicinity of a TAP minimum or pure state.

8 pages, 6 figures, modified text and figures, references added

References in corpus (7)

• Marginal Stability in Structural, Spin and Electron Glasses
• Mean-field message-passing equations in the Hopfield model and its generalizations
• Finite size corrections in the Sherrington-Kirkpatrick model
• Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
• The metastable minima of the Heisenberg spin glass in a random magnetic field
• Distribution of time scales in the Sherrington-Kirkpatrick model
• Evidence for a Vanishing Complexity of the Sherrington-Kirkpatrick model

Cited by in corpus (3)

• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Classical Annealing of Sherrington-Kirkpatrick Spin Glass Using Suzuki-Kubo Mean-field Ising Dynamics
• Free energy barriers in the Sherrington-Kirkpatrick model