Searching for the Gardner Transition in Glassy Glycerol

Dynamic Gardner cross-over in a simple glass

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.

How to count in hierarchical landscapes: A full solution to mean-field complexity

We derive the general solution for counting the stationary points of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with multistep replica symmetry breaking and one with full replica symmetry breaking.

Johari-Goldstein β relaxation in glassy dynamics originates from two-scale energy landscape

Supercooled liquids undergo complicated structural relaxation processes, which have been a long-standing problem in both experimental and theoretical aspects of condensed matter physics. In particular, past experiments widely observed for many types of molecular liquids that relaxation dynamics separated into two distinct processes at low temperatures. One of the possible interpretations is that this separation originates from the two-scale hierarchical topography of the potential energy landscape; however, it has never been verified. Molecular dynamics simulations are a promising approach to tackle this issue, but we must overcome laborious difficulties. First, we must handle a model of molecular liquids that is computationally demanding compared to simple spherical models, which have been intensively studied but show only a slower process: α relaxation. Second, we must reach a sufficiently low-temperature regime where the two processes become well-separated. Here, we handle an asymmetric dimer system that exhibits a faster process: Johari-Goldstein β relaxation. Then, we employ the parallel tempering method to access the low-temperature regime. These laborious efforts enable us to investigate the potential energy landscape in detail and unveil the first direct evidence of the topographic hierarchy that induces the β relaxation. We also successfully characterize the microscopic motions of particles during each relaxation process. Finally, we study the correlation between low-frequency modes and two relaxation processes. Our results establish a fundamental and comprehensive understanding of experimentally observed relaxation dynamics in supercooled liquids.

Glassy dynamics in polyalcohols: intermolecular simplicity vs. intramolecular complexity

Using depolarized light scattering, we have recently shown that structural relaxation in a broad range of supercooled liquids follows, to good approximation, a generic line shape with high-frequency power law ω^-1/2. We now continue this study by investigating a systematic series of polyalcohols (PAs), frequently used as model-systems in glass-science, i.a., because the width of their respective dielectric loss spectra varies strongly along the series. Our results reveal that the microscopic origin of the observed relaxation behavior varies significantly between different PAs: while short-chained PAs like glycerol rotate as more or less rigid entities and their light scattering spectra follow the generic shape, long-chained PAs like sorbitol display pronounced intramolecular dynamic contributions on the time scale of structural relaxation, leading to systematic deviations from the generic shape. Based on these findings we discuss an important limitation for observing the generic shape in a supercooled liquid: the dynamics that is probed needs to reflect the intermolecular dynamic heterogeneity, and must not be superimposed by effects of intramolecular dynamic heterogeneity.

Probing Gardner Physics in an Active Quasithermal Pressure-Controlled Granular System of Noncircular Particles

To search for experimental signals of the Gardner crossover, an active quasithermal granular glass is constructed using a monolayer of air-fluidized star-shaped particles. The pressure of the system is controlled by adjusting the tension exerted on an enclosing boundary. Velocity distributions of the internal particles and the scaling of the pressure, density, effective temperature, and relaxation time are examined, demonstrating that the system has key features of a thermal system. Using a pressure-based quenching protocol that brings the system into deeper glassy states, signals of the Gardner crossover are detected via cage size and separation order parameters for both particle positions and orientations, offering experimental evidence of Gardner physics for a system of anisotropic quasithermal particles in a low spatial dimension.

Experimental observations of marginal criticality in granular materials

SignificanceAmorphous materials, such as grains, foams, colloids, and glasses, are ubiquitous in nature and our daily life. They can undergo glass transitions or jamming transitions to obtain rigidity either by fast quench or compression, but show subtle changes in the structures compared to the liquid states or liquid-like states. Recent progress on the first-principle replica theory unifies the glass transition and the jamming transition and points out the marginal phase with fractal free-energy landscape within the stable glass phase. Independently, marginal stability analysis predicts the relations between the exponents of the marginal phase. Here, we perform experiments with photoelastic disks and provide direct evidence of these theories in real-world amorphous materials.

Numerical test of the replica-symmetric Hamiltonian for correlations of the critical state of spin glasses in a field

A growing body of evidence indicates that the sluggish low-temperature dynamics of glass formers (e.g., supercooled liquids, colloids, or spin glasses) is due to a growing correlation length. Which is the effective field theory that describes these correlations? The natural field theory was drastically simplified by Bray and Roberts in 1980. More than 40 years later, we confirm the tenets of Bray and Roberts's theory by studying the Ising spin glass in an externally applied magnetic field, both in four spatial dimensions (data obtained from the Janus collaboration) and on the Bethe lattice.