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Fractal free energy landscapes in structural glasses.
- P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, F. Zamponi
- Materials ScienceNature Communications
- 24 April 2014
It is shown, using theory and numerical simulation, that the landscape is much rougher than is classically assumed and undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming.
Mean-field theory of hard sphere glasses and jamming
Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider…
Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
Comparing mean-field predictions with the finite-dimensional simulations, this work identifies robust aspects of the description of hard spheres around the dynamical, Gardner and jamming transitions and uncover its more sensitive features.
Theory of Simple Glasses: Exact Solutions in Infinite Dimensions
This pedagogical and self-contained text describes the modern mean field theory of simple structural glasses. The book begins with a thorough explanation of infinite-dimensional models in statistical…
Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution
The general replica equations that describe infinite-dimensional hard spheres at any level of replica symmetry breaking (RSB) and in particular in the fullRSB scheme are derived, showing that the analogy between spin glasses and structural glasses conjectured by Kirkpatrick, Thirumalai and Wolynes is realized in a strong sense in the mean-field limit.
Universal spectrum of normal modes in low-temperature glasses
- S. Franz, G. Parisi, P. Urbani, F. Zamponi
- PhysicsProceedings of the National Academy of Sciences
- 5 June 2015
An analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron, and identifies two distinct classes of soft modes that are related to isostaticity and appear only in the close vicinity of the jamming transition.
Jamming criticality revealed by removing localized buckling excitations.
This work constructs isostatic jammed packings with extremely high accuracy, and introduces a simple criterion to separate the contribution of particles that give rise to localized buckling excitations from the others, revealing the remarkable dimensional robustness of mean-field marginality and its associated criticality.
Universal microstructure and mechanical stability of jammed packings.
This work provides a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres and discovers a set of new scaling relations that connect the behavior of particles bearing small forces and those bearing no force but that are almost in contact.
Chaotic Hypothesis, Fluctuation Theorem and Singularities
The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application…
Tipping Points in Macroeconomic Agent-Based Models
The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABMs) can reproduce. We propose a methodology, inspired by statistical physics, that…