The role of the Becchi-Rouet-Stora-Tyutin supersymmetry in the calculation of the complexity for the Sherrington-Kirkpatrick model

Abstract

The Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry is a powerful tool for the calculation of the complexity of metastable states in glassy systems, and it is particularly useful to uncover the relationships between complexity and standard thermodynamics. In this work we compute the Thouless-Anderson-Palmer complexity of the Sherrington-Kirkpatrick model at the quenched level, by using the BRST supersymmetry. We show that the complexity calculated at K steps of replica symmetry breaking is strictly related to the static free energy at K+1 steps of replica symmetry breaking. The supersymmetry therefore provides a prescription to obtain the complexity of the TAP states from the standard static free energy, even in models which are solved by more than one step of replica symmetry breaking. This recipe states that the complexity is given by the Legendre transform of the static free energy, where the Legendre parameter is the largest replica symmetry breaking point of the overlap matrix.

arXiv comment14 pages

References in corpus (6)

• The structural glass transition and the entropy of the metastable states
• On the stationary points of the TAP free energy
• Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices
• Quenched complexity of the p-spin spherical spin-glass with external magnetic field
• On the formal equivalence of the TAP and thermodynamic methods in the SK model
• On the number of metastable states in spin glasses

Cited by in corpus (13)

• Instability of one-step replica-symmetry-broken phase in satisfiability problems
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• Numerical study of metastable states in Ising spin glasses
• Supersymmetric quenched complexity in the Sherrington-Kirkpatrick model
• Marginal States in Mean Field Glasses
• Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model
• How to count in hierarchical landscapes: a 'full' solution to mean-field complexity
• Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
• Tap Complexity, the Cavity Method and Supersymmetry
• Replica symmetry breaking, complexity and spin representation in the generalized random energy model
• Regge theory and statistical mechanics
• The Complexity of Vector Spin Glasses
• On the topology of solutions to random continuous constraint satisfaction problems