Browsing by Author "Zamponi, F"

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    Exact theory of dense amorphous hard spheres in high dimension. III. the full replica symmetry breaking solution
    (Journal of Statistical Mechanics: Theory and Experiment, 2014-10-01) Charbonneau, P; Kurchan, J; Parisi, G; Urbani, P; Zamponi, F
    © 2014 IOP Publishing Ltd. In the first part of this paper, we derive 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. We show that these equations are formally very similar to the ones that have been derived for spin glass models, thus 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. We also suggest how the computation could be generalized in an approximate way to finite-dimensional hard spheres. In the second part of the paper, we discuss the solution of these equations and we derive from it a number of physical predictions. We show that, below the Gardner transition where the 1RSB solution becomes unstable, a fullRSB phase exists and we locate the boundary of the fullRSB phase. Most importantly, we show that the fullRSB solution predicts correctly that jammed packings are isostatic, and allows one to compute analytically the critical exponents associated with the jamming transition, which are missed by the 1RSB solution. We show that these predictions compare very well with numerical results.
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    Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
    (2017-04-01) Charbonneau, P; Kurchan, J; Parisi, G; Urbani, P; Zamponi, F
    Despite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution in the mean-field limit of infinite spatial dimension, and numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the description and uncover its more sensitive features. We conclude with a brief overview of ongoing research.