Dynamical TAP approach to mean field glassy systems

1999/09/30 by Giulio Biroli · 1 citation
Materials Science · Physics and Astronomy · #Context (archaeology) #Dynamical system (definition) #Dynamical systems theory #Energy (signal processing) #Field (mathematics) #Material Dynamics and Properties #Mean field theory #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/32/48/301

published as J. Phys. A: Math. Gen. 32 (1999) 8365 · final version, 21 pages, 1 eps figure

openalex publication_date 1999/11/17 · arxiv created 1999/12/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The Thouless, Anderson and Palmer (TAP) approach to thermodynamics of mean field spin glasses is generalized to dynamics. A method to compute the dynamical TAP equations is developed and applied to the p -spin spherical model. In this context we show to what extent the dynamics can be represented as an evolution in the free energy landscape. In particular the relationship between the long-time dynamics and the local properties of the free energy landscape shows up explicitly within this approach. Conversely, by an instantaneous normal modes analysis we show that the local properties of the energy landscape seen by the system during its dynamical evolution do not change qualitatively at the dynamical transition.

Citations

• Solution of 'Solvable model of a spin glass'
• The number of solutions of the Thouless-Anderson-Palmer equations forp-spin-interaction spin glasses
• Relationship between long timescales and the static free-energy in the Hopfield model
• Electrons in disordered systems and the theory of localization
• Effective action for composite operators

Cited by

• Rare Trajectories in a Prototypical Mean-field Disordered Model: Insights into Landscape and Instantons