Numerical Study of Metastable States in Ising Spin Glasses

2003/12/19 by Andrea Cavagna, Irene Giardina, Giorgio Parisi · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Ising model #Ising spin #Limit (mathematics) #Mathematics #Metastability #Order (exchange) #Physics #Quantum mechanics #Saddle #Saddle point #Spin (aerodynamics) #Spin glass #Supersymmetry #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.92.120603

published as Phys. Rev. Lett. 92, 120603 (2004)

arxiv created 2003/12/19 · openalex publication_date 2004/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all nonparamagnetic stationary points of the free energy are organized into pairs, consisting of a minimum and an order 1 saddle, which coalesce in the thermodynamic limit. Within the annealed approximation, the entropic contribution of these states, that is the complexity, is compatible with the supersymmetry-breaking calculation performed by Bray and Moore [J. Phys. C 13, L469 (1980)]]. This result indicates that the supersymmetry is spontaneously broken in the Sherrington-Kirkpatrick model.

Citations

• Solution of 'Solvable model of a spin glass'
• The role of the Becchi–Rouet–Stora–Tyutin supersymmetry in the calculation of the complexity for the Sherrington–Kirkpatrick model
• Perspective on the glass transition

Cited by

• Realizable solutions of the Thouless-Anderson-Palmer equations
• Time dependent local field distribution and metastable states in the SK-spin-glass
• Incompleteness of the Thouless, Anderson, and Palmer mean-field description of the spin-glass phase