On the formal equivalence of the TAP and thermodynamic methods in the SK model

Abstract

We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469; De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry, we prove the general equivalence of TAP and replica partition functions, and show that the annealed calculation of the TAP complexity is formally identical to the quenched thermodynamic calculation of the free energy at one step level of replica symmetry breaking. The complexity we obtain by means of the BRST symmetry turns out to be considerably smaller than the previous non-symmetric value.

arXiv comment17 pages, 3 figures

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• The structural glass transition and the entropy of the metastable states
• On the stationary points of the TAP free energy
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• From inherent structures to pure states: some simple remarks and examples
• Quenched complexity of the p-spin spherical spin-glass with external magnetic field
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Cited by in corpus (24)

• The Complexity of Ising Spin Glasses
• Complexity in Mean-Field Spin-Glass Models: Ising $p$-spin
• Numerical study of metastable states in Ising spin glasses
• Universality Classes of Critical Points in Constrained Glasses
• Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation
• Supersymmetric quenched complexity in the Sherrington-Kirkpatrick model
• On Spin-Glass Complexity
• On the TAP free energy in the mixed $p$-spin models
• Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model
• The role of the Becchi-Rouet-Stora-Tyutin supersymmetry in the calculation of the complexity for the Sherrington-Kirkpatrick model
• Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
• On Supersymmetry Breaking in the Computation of the Complexity
• Cavity Method for Supersymmetry Breaking Spin Glasses
• Tap Complexity, the Cavity Method and Supersymmetry
• Dynamics and geometric properties of the k-Trigonometric model
• Off-equilibrium confined dynamics in a glassy system with level-crossing states
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Variational perturbation and extended Plefka approaches to dynamics on random networks: the case of the kinetic Ising model
• Thresholds of descending algorithms in inference problems
• The Complexity of Vector Spin Glasses
• Zero-Temperature Limit of the SUSY-breaking Complexity in Diluted Spin-Glass Models
• Spin Glass Theory: numerical and experimental results in three-dimensional systems
• Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses
• Thermodynamic origin of order parameters in mean-field models of spin glasses