2003/09/30 by Timo Aspelmeier, T. Aspelmeier, A. J. Bray +2
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.92.087203
published as Phys. Rev. Lett. 92, 087203 (2004) · Typos corrected
arxiv created 2003/09/30 · openalex publication_date 2004/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We compute the complexity [logarithm of the number of Thouless-Anderson-Palmer (TAP) states] associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent with the Morse theorem on the total number of turning points, and have the value given by Bray and Moore [J. Phys. C, ()]]. In the thermodynamic limit, TAP states of all free energies become marginally stable.