Incompleteness of the Thouless, Anderson, and Palmer mean-field description of the spin-glass phase

Abstract

We analyze the low-temperature behavior of mean-field equations of Thouless, Anderson, and Palmer (TAP). We demonstrate that degeneracy in free energy makes the low-temperature TAP states unstable. Different solutions of the TAP equations, independent in the TAP approach, become coupled if an infinitesimal interaction between them is introduced. By means of real spin replicas we derive a self-averaging free energy free of unstable states with local magnetizations and homogeneous overlap susceptibilities between different spin replicas as order parameters. We thereby extend the TAP approach to a consistent description of the spin-glass phase for all configurations of spin couplings with (marginally) stable and thermodynamically homogeneous free energy.

arXiv commentREVTeX4, 14 pages, No figures

References in corpus (8)

• The Thermodynamic Limit in Mean Field Spin Glass Models
• The Complexity of Ising Spin Glasses
• Numerical study of metastable states in Ising spin glasses
• On Spin-Glass Complexity
• Modified TAP equations for the SK spin glass
• Modified Thouless-Anderson-Palmer equations for the Sherrington-Kirkpatrick spin glass: Numerical solutions
• Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space
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Cited by in corpus (3)

• The Parisi formula completed
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• Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model