Marginal States in Mean Field Glasses

Abstract

We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In particular, we give a physical interpretation of the two-group replica symmetry breaking scheme and confirm it by establishing the relation to the cavity method and to the counting of solutions of the Thouless-Anderson-Palmer equations. We show how these methods all incorporate the presence of a soft mode in the free energy landscape and interpret the occurring order parameter functions in terms of correlations between the soft mode and the local magnetizations. The general formalism is applied to the prototypical case of the Sherrington-Kirkpatrick-model where we re-examine the physical properties of marginal states under a new perspective.

27 pages, 8 figures

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Cited by in corpus (20)

• Phase Transitions in the Coloring of Random Graphs
• A Landscape Analysis of Constraint Satisfaction Problems
• Complexity of waves in nonlinear disordered media
• Generalization of the cavity method for adiabatic evolution of Gibbs states
• Complex energy landscapes in spiked-tensor and simple glassy models: ruggedness, arrangements of local minima and phase transitions
• Amorphous-amorphous transition and the two-step replica symmetry breaking phase
• The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media
• Hessian spectrum at the global minimum of high-dimensional random landscapes
• Time Dependent Local Field Distribution and Metastable States in the SK-Spin-Glass
• Distribution of rare saddles in the $p$-spin energy landscape
• On Equilibrium Dynamics of Spin-Glass Systems
• The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour
• Manifolds in high dimensional random landscape: complexity of stationary points and depinning
• Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses
• Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum
• On the topology of solutions to random continuous constraint satisfaction problems
• Free energy barriers in the Sherrington-Kirkpatrick model
• Far-from-equilibrium complex landscapes
• A replica trick for rare samples
• Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model