# Browsing by Author "Zamponi, Francesco"

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Item Restricted Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.(Phys Rev E Stat Nonlin Soft Matter Phys, 2010-11) Jin, Yuliang; Charbonneau, Patrick; Meyer, Sam; Song, Chaoming; Zamponi, FrancescoThe isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song et al., Nature (London) 453, 629 (2008)] is generalized to arbitrary dimension d using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling ϕ∼d2(-d) is consistent with that of other approaches, such as replica theory and density-functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.Item Open Access Dimensional dependence of the Stokes-Einstein relation and its violation(Journal of Chemical Physics, 2013-10-28) Charbonneau, Benoit; Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, FrancescoWe generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension d u = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem. © 2013 AIP Publishing LLC.Item Open Access Dimensional study of the caging order parameter at the glass transition.(Proc Natl Acad Sci U S A, 2012-08-28) Charbonneau, Patrick; Ikeda, Atsushi; Parisi, Giorgio; Zamponi, FrancescoThe glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed upon regarding why a fluid becomes sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension d, we find the cage to keep a nontrivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is qualitatively supported here and non-mean-field corrections are found to remain small on decreasing d, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.Item Open Access Equilibrium fluctuations in mean-field disordered models.(Physical review. E, 2022-08) Folena, Giampaolo; Biroli, Giulio; Charbonneau, Patrick; Hu, Yi; Zamponi, FrancescoMean-field models of glasses that present a random first order transition exhibit highly nontrivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states. We first test and compare our analytical results with numerical simulation results for the p-spin spherical model and the random orthogonal model, and then analyze the random Lorentz gas. In all cases, a strong quantitative agreement is obtained. Our analysis thus provides a robust scheme for identifying the key finite-size (or finite-dimensional) corrections to the mean-field treatment of these paradigmatic glass models.Item Open Access Fractal free energy landscapes in structural glasses.(Nat Commun, 2014-04-24) Charbonneau, Patrick; Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, FrancescoGlasses are amorphous solids whose constituent particles are caged by their neighbours and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marginal stability on approaching jamming. Critical exponents for the basin width, the weak force distribution and the spatial spread of quasi-contacts near jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control what features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here.Item Open Access Gardner physics in amorphous solids and beyond.(The Journal of chemical physics, 2019-07) Berthier, Ludovic; Biroli, Giulio; Charbonneau, Patrick; Corwin, Eric I; Franz, Silvio; Zamponi, FrancescoOne of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain mean-field spin glass models, its materials relevance was only realized when a systematic effort to relate glass formation and jamming was undertaken. A number of nontrivial physical signatures associated with the Gardner transition have since been considered in various areas, from models of structural glasses to constraint satisfaction problems. This perspective surveys these recent advances and discusses the novel research opportunities that arise from them.Item Open Access Glass transition and random close packing above three dimensions.(Phys Rev Lett, 2011-10-28) Charbonneau, Patrick; Ikeda, Atsushi; Parisi, Giorgio; Zamponi, FrancescoMotivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimensions.Item Open Access Growing timescales and lengthscales characterizing vibrations of amorphous solids.(Proc Natl Acad Sci U S A, 2016-07-26) Berthier, Ludovic; Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Seoane, Beatriz; Zamponi, FrancescoLow-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a boson peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time- and lengthscales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.Item Open Access Hopping and the Stokes-Einstein relation breakdown in simple glass formers.(Proc Natl Acad Sci U S A, 2014-10-21) Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, FrancescoOne of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.Item Open Access Interplay between percolation and glassiness in the random Lorentz gas.(Physical review. E, 2021-03) Biroli, Giulio; Charbonneau, Patrick; Corwin, Eric I; Hu, Yi; Ikeda, Harukuni; Szamel, Grzegorz; Zamponi, FrancescoThe random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media that exhibits a continuous localization transition controlled by void space percolation. The RLG also provides a toy model of particle caging, which is known to be relevant for describing the discontinuous dynamical transition of glasses. In order to clarify the interplay between the seemingly incompatible percolation and caging descriptions of the RLG, we consider its exact mean-field solution in the infinite-dimensional d→∞ limit and perform numerics in d=2...20. We find that for sufficiently high d the mean-field caging transition precedes and prevents the percolation transition, which only happens on timescales diverging with d. We further show that activated processes related to rare cage escapes destroy the glass transition in finite dimensions, leading to a rich interplay between glassiness and percolation physics. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of particle hopping in structural glasses.Item Open Access Jamming criticality revealed by removing localized buckling excitations.(Phys Rev Lett, 2015-03-27) Charbonneau, Patrick; Corwin, Eric I; Parisi, Giorgio; Zamponi, FrancescoRecent theoretical advances offer an exact, first-principles theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small interparticle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the interparticle gaps is known to be constant in all spatial dimensions d-including the physically relevant d=2 and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.Item Open Access Local dynamical heterogeneity in glass formers(2021-09-24) Biroli, Giulio; Charbonneau, Patrick; Folena, Giampaolo; Hu, Yi; Zamponi, FrancescoWe study the local dynamical fluctuations in glass-forming models of particles embedded in $d$-dimensional space, in the mean-field limit of $d\to\infty$. Our analytical calculation reveals that single-particle observables, such as squared particle displacements, display divergent fluctuations around the dynamical (or mode-coupling) transition, due to the emergence of nontrivial correlations between displacements along different directions. This effect notably gives rise to a divergent non-Gaussian parameter, $\alpha_2$. The $d\to\infty$ local dynamics therefore becomes quite rich upon approaching the glass transition. The finite-$d$ remnant of this phenomenon further provides a long sought-after, first-principle explanation for the growth of $\alpha_2$ around the glass transition that is \emph{not based on multi-particle correlations}.Item Open Access Local Dynamical Heterogeneity in Simple Glass Formers.(Physical review letters, 2022-04) Biroli, Giulio; Charbonneau, Patrick; Folena, Giampaolo; Hu, Yi; Zamponi, FrancescoWe study the local dynamical fluctuations in glass-forming models of particles embedded in d-dimensional space, in the mean-field limit of d→∞. Our analytical calculation reveals that single-particle observables, such as squared particle displacements, display divergent fluctuations around the dynamical (or mode-coupling) transition, due to the emergence of nontrivial correlations between displacements along different directions. This effect notably gives rise to a divergent non-Gaussian parameter, α_{2}. The d→∞ local dynamics therefore becomes quite rich upon approaching the glass transition. The finite-d remnant of this phenomenon further provides a long sought-after, first-principle explanation for the growth of α_{2} around the glass transition that is not based on multiparticle correlations.Item Open Access Mean-Field Caging in a Random Lorentz Gas.(The journal of physical chemistry. B, 2021-06-07) Biroli, Giulio; Charbonneau, Patrick; Hu, Yi; Ikeda, Harukuni; Szamel, Grzegorz; Zamponi, FrancescoThe random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional,*d*→ ∞ limit: the localization transition is then expected to be*continuous*for the former and*discontinuous*for the latter. As a putative resolution, we have recently suggested that, as*d*increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite-*d*perturbative and nonperturbative (instantonic) corrections [Biroli et al.*Phys. Rev. E*2021, 103, L030104]. Here, we expand on the*d*→ ∞ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/*d*correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that, although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the*d*→ ∞ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.Item Open Access Numerical detection of the Gardner transition in a mean-field glass former.(Phys Rev E Stat Nonlin Soft Matter Phys, 2015-07) Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Rainone, Corrado; Seoane, Beatriz; Zamponi, FrancescoRecent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.Item Open Access Origin of Ultrastability in Vapor-Deposited Glasses.(Physical review letters, 2017-11) Berthier, Ludovic; Charbonneau, Patrick; Flenner, Elijah; Zamponi, FrancescoGlass films created by vapor-depositing molecules onto a substrate can exhibit properties similar to those of ordinary glasses aged for thousands of years. It is believed that enhanced surface mobility is the mechanism that allows vapor deposition to create such exceptional glasses, but it is unclear how this effect is related to the final state of the film. Here we use molecular dynamics simulations to model vapor deposition and an efficient Monte Carlo algorithm to determine the deposition rate needed to create ultrastable glassy films. We obtain a scaling relation that quantitatively captures the efficiency gain of vapor deposition over bulk annealing, and demonstrates that surface relaxation plays the same role in the formation of vapor-deposited glasses as bulk relaxation does in ordinary glass formation.Item Open Access Three simple scenarios for high-dimensional sphere packings.(Physical review. E, 2021-12) Charbonneau, Patrick; Morse, Peter K; Perkins, Will; Zamponi, FrancescoBased on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: in scenario A, crystallization is impeded and the glass phase constitutes the densest packing; in scenario B, crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible; and in scenario C, crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings for dimension d=3-10 using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close packing tend to support scenario C. We additionally confirm that the crystal equation of state is dominated by the free-volume expansion and that a meaningful polynomial correction can be formulated.Item Open Access Universal microstructure and mechanical stability of jammed packings.(Phys Rev Lett, 2012-11-16) Charbonneau, Patrick; Corwin, Eric I; Parisi, Giorgio; Zamponi, FrancescoThe mechanical properties of jammed packings depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres. In particular we discover 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. By performing systematic investigations for spatial dimensions d=3-10, in a wide density range and using different preparation protocols, we show that these scalings are indeed universal. We therefore establish clear milestones for the emergence of a complete microscopic theory of jamming. This description is also crucial for high-precision force experiments in granular systems.Item Open Access Universal Non-Debye Scaling in the Density of States of Amorphous Solids.(Phys Rev Lett, 2016-07-22) Charbonneau, Patrick; Corwin, Eric I; Parisi, Giorgio; Poncet, Alexis; Zamponi, FrancescoAt the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.