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

Abstract

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.

6 pages, 7 figures

References in corpus (13)

• Mean field theory of hard sphere glasses and jamming
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• Phase Transitions in the Coloring of Random Graphs
• A Landscape Analysis of Constraint Satisfaction Problems
• Hiding Quiet Solutions in Random Constraint Satisfaction Problems
• On the freezing of variables in random constraint satisfaction problems
• Generalization of the cavity method for adiabatic evolution of Gibbs states
• Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
• Potts Glass on Random Graphs
• Quiet Planting in the Locked Constraint Satisfaction Problems
• Random subcubes as a toy model for constraint satisfaction problems
• Exhaustive enumeration unveils clustering and freezing in random 3-SAT
• Off-equilibrium confined dynamics in a glassy system with level-crossing states

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