Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems

Details Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems

2009-09-21

arxiv.org/abs/0909.3820v3

2010 EPL 90 66002

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 7 figures

Scientific paper

10.1209/0295-5075/90/66002

We introduce a generalization of the cavity, or Bethe-Peierls, method that allows to follow Gibbs states when an external parameter, e.g. the temperature, is adiabatically changed. This allows to obtain new quantitative results on the static and dynamic behavior of mean field disordered systems such as models of glassy and amorphous materials or random constraint satisfaction problems. As a first application, we discuss the residual energy after a very slow annealing, the behavior of out-of-equilibrium states, and demonstrate the presence of temperature chaos in equilibrium. We also explore the energy landscape, and identify a new transition from an computationally easier canyons-dominated region to a harder valleys-dominated one.

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