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

2005/12/31 by V. Janiš, V. Janis
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Condensed matter physics #Degeneracy (biology) #Field (mathematics) #Homogeneous #Mathematics #Mean field theory #Phase (matter) #Physics #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Spin glass #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.74.054207

published as Phys. Rev. B74, 054207 (2006) · REVTeX4, 14 pages, No figures

openalex publication_date 2006/08/16 · arxiv created 2006/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 exchange with (marginally) stable and thermodynamically homogeneous free energy.

Citations

• The Thermodynamic Limit in Mean Field Spin Glass Models
• Spin-Glass Complexity
• Complexity of Ising Spin Glasses
• Solution of 'Solvable model of a spin glass'
• SPECTRA OF RANDOM SELF ADJOINT OPERATORS
• Numerical Study of Metastable States in Ising Spin Glasses
• Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space