Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model

Abstract

The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz corresponds to require Becchi-Rouet-Stora-Tyutin supersymmetry. The complexity computed this way is the Legendre transform of the free energy averaged over the quenched disorder. The stability analysis shows that this complexity is inconsistent at any free energy level but the equilibirum one. The further problem of building a physically well defined solution not invariant under supersymmetry and predicting an extensive number of metastable states is also discussed.

19 pages, 13 figures. Some formulas added corrected, changes in discussion and conclusion, one figure added

References in corpus (7)

• The Complexity of Ising Spin Glasses
• Chaos in temperature in the Sherrington-Kirkpatrick model
• On the formal equivalence of the TAP and thermodynamic methods in the SK model
• The Complexity of the Spherical $p$-spin spin glass model, revisited
• Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation
• On Spin-Glass Complexity
• The role of the Becchi-Rouet-Stora-Tyutin supersymmetry in the calculation of the complexity for the Sherrington-Kirkpatrick model

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• The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition
• Mean field theory for the three-dimensional Coulomb glass
• Complexity in Mean-Field Spin-Glass Models: Ising $p$-spin
• Low temperature solution of the Sherrington-Kirkpatrick model
• Marginal States in Mean Field Glasses
• Mean field theory of superglasses
• Tap Complexity, the Cavity Method and Supersymmetry
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Expansion of the Gibbs potential for quantum many-body systems: General formalism with applications to the spin glass and the weakly non-ideal Bose gas
• Thresholds of descending algorithms in inference problems
• The Sherrington-Kirkpatrick model near T_c and near T=0
• Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model
• Emergence of near-TAP free energy functional in the SK model at high temperature