# Browsing by Author "Biroli, Giulio"

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Item Open Access Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic LatticesBiroli, Giulio; Charbonneau, Patrick; Hu, YiRecent advances on the glass problem motivate reexamining classical models of percolation. Here, we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the upper critical dimension of simple percolation, d_u=6. Using theory and simulations, we consider the scaling regime part, and obtain that both caging and subdiffusion scale logarithmically for d >= d_u. The theoretical derivation considers Bethe lattices with generalized connectivity and a random graph model, and employs a scaling analysis to confirm that logarithmic scalings should persist in the infinite dimension limit. The computational validation employs accelerated random walk simulations with a transfer-matrix description of diffusion to evaluate directly the dynamical critical exponents below d_u as well as their logarithmic scaling above d_u. Our numerical results improve various earlier estimates and are fully consistent with our theoretical predictions.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 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 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 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.