Low-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.glass transition | disordered solids | Gardner transition | computer simulations | hard spheres U nderstanding the nature of the glass transition, which describes the gradual transformation of a viscous liquid into an amorphous solid, remains an open challenge in condensed matter physics (1, 2). As a result, the glass phase itself is not well understood either. The main challenge is to connect the localized, or "caged," dynamics that characterizes the glass transition to the low-temperature anomalies that distinguish amorphous solids from their crystalline counterparts (3-7). Recent theoretical advances, building on the random first-order transition approach (8), have led to an exact mathematical description of both the glass transition and the amorphous phases of hard spheres in the mean-field limit of infinite-dimensional space (9). A surprising outcome has been the discovery of a novel phase transition inside the amorphous phase, separating the localized states produced at the glass transition from their inherent structures. This Gardner transition (10), which marks the emergence of a fractal hierarchy of marginally stable glass states, can be viewed as a glass transition deep within a glass, at which vibrational motion dramatically slows down and becomes spatially correlated (11). Although these theoretical findings promise to explain and unify the emergence of low-temperature anomalies in amorphous solids, the gap remains wide between mean-field calculations (9, 11) and experimental work. Here, we provide direct numerical evidence that vibrational motion in a simple 3D glass-former becomes anomalous at a well-defined location inside the glass phase. In particular, we report the rapid growth of a relaxation time related to cooperative vibrations, a nontrivial change in the probability distribution function of a global order parameter, and the rapid growth of a correlation length. We also relate these findings to observed anomalies in low-temperature laboratory glasses. These re...

One 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.activated processes | random first-order transition | cavity method G lasses are amorphous materials whose rigidity emerges from the mutual caging of their constituent particles-be they atoms, molecules, colloids, grains, or cells. Although glasses are ubiquitous, the microscopic description of their formation, rheology, and other dynamical features is still far from satisfying. Developing a more complete theoretical framework would not only resolve epistemological wrangles (1), but also improve our material control and design capabilities. However, such a research program remains fraught with challenges. Conventional paradigms based on perturbative expansions around the low-density, ideal gas limit (for moderately dense gases and liquids) or on harmonic expansions around an ideal lattice (for crystals) fail badly. Because dense amorphous materials interact strongly, low-density expansions are unreliable, whereas harmonic expansions lack reference equilibrium particle positions. These fundamental difficulties must somehow be surmounted to describe the dynamical processes at play in glass formation.A celebrated strategy for studying phase transitions is to consider first their mean-field description, which becomes exact when the spatial dimension d of the system goes to infinity (2), before including corrections to this description. In that spirit, we open with the d → ∞ "ideal" random first-order transition (iRFOT) scenario, which, based on the analysis of simple models, brings together static-(3-5) and dynamics-based (mode-coupling) (6) results for glass formation (reviews in refs. 7 and 8) ...

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit.Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the "freezing point" in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the "entropy of fusion". This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics. 1Since the time of Kepler it is thought that the most efficient packing of monodisperse spherical grains is the face centered cubic (FCC) arrangement with a density of 74 % [1].Thus, we might expect that spherical particles will tend to optimize the space they occupy by crystallizing up to this limiting density. Instead, granular systems of spheres arrest in a random close packing (RCP), which is not optimal but occupies ∼64% of space [2]. Previous studies have derived geometric statistical models to map the microscopic origin of the much debated 64% density of RCP [2][3][4][5][6][7][8][9]. However, the physical laws that govern its creation and render it the most favorable state for randomly packed particles remains one of the most salient questions in understanding all of jammed matter [3][4][5]8]. For instance, while it is known that systems in equilibrium follow energy minimization and entropy maximization to reach a steady state, the mechanism by which RCP is achieved is much sought after.Here we propose a thermodynamic view of the sphere packing problem where the experimentally observed RCP can be viewed as a manifestation of a singularity in a first-order phase transition. Despite the inherent out-of-equilibrium nature of granular matter, the formation of a jammed crystal can be mapped to a thermodynamic process that occurs at a precise compactivity where the volume and entropy are discontinuous.We investigate mechanically stable packings ranging from the lowest possible volume fraction of random loose packing (RLP) [10] to FCC. We numerically generate packings of N =10,000 spherical particles of radius R = 100µm in a periodically repeated cube. Initially, we use the Lubachevsky-Stillinger (LS) [11,12] and force-biased (FBA) [13] algorithms to generate amorphous configurations of unjammed...

When two immiscible polymers are brought into intimate contact, highly localized mixing of polymer chains creates an “interphase” region. Materials that are entirely interphase are fabricated by forced‐assembly using layer‐multiplying coextrusion to form assemblies of thousands of nanolayers. Analysis of the interphase materials with conventional methods of polymer analysis confirms certain theoretical predictions for the first time. The unique properties of the new interphase materials result from lower free volume than the constituents.Atomic force microscopy phase image from the cross‐section of a PC/PMMA nanolayer film with 4096 layers and average layer thickness of 25 nm.magnified imageAtomic force microscopy phase image from the cross‐section of a PC/PMMA nanolayer film with 4096 layers and average layer thickness of 25 nm.

We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.

Recent 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.

A stability-reversibility map unifies the response of amorphous solids to volume and shear deformations.

For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of amorphous solids revealed the possibility of unexpectedly complex free-energy landscapes where the simple harmonic picture breaks down. Here we demonstrate that standard rheological techniques can be used as powerful tools to examine nontrivial consequences of such complex free-energy landscapes. By extensive numerical simulations on a hard sphere glass under quasistatic shear at finite temperatures, we show that above the so-called Gardner transition density, the elasticity breaks down, the stress relaxation exhibits slow, and ageing dynamics and the apparent shear modulus becomes protocol-dependent. Being designed to be reproducible in laboratories, our approach may trigger explorations of the complex free-energy landscapes of a large variety of amorphous materials.