Dynamical TAP approach to mean field glassy systems

TL;DR

This paper extends the TAP approach to the dynamics of mean field spin-glasses, providing a method to analyze how systems evolve within their free energy landscape, with applications to the p-spin spherical model.

Contribution

It develops a dynamical TAP framework for mean field spin-glasses and applies it to the p-spin spherical model, linking dynamics to the free energy landscape.

Findings

Dynamics can be represented as evolution in the free energy landscape.

Long-time dynamics relate to local properties of the energy landscape.

Local landscape properties do not change qualitatively at the dynamical transition.

Abstract

The Thouless, Anderson, Palmer (TAP) approach to thermodynamics of mean field spin-glasses is generalised 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.