Session R3: Glass and Jamming Transitions

The Gardner Transition: A new approach for understanding low-temperature glasses

Recent theoretical advances in the mean-field theory of glasses predict the existence deep in the glass phase of a novel phase transition, a so-called Gardner transition. This transition signals the emergence of a complex free energy landscape composed of a marginally stable hierarchy of sub-basins within a broad glass metabasin. It is thus the onset of marked changes in thermal and transport properties of glasses, and ultimately leads to the unusual critical behavior at jamming. The Gardner transition itself is immediately related to a diverging (i) characteristic relaxation time, (ii) caging susceptibility and (iii) correlation length of the caging heterogeneity as well as aging, even in well-thermalized glasses. We have detected some of these signatures both in a mean-field model and in standard hard-sphere glass formers. We find the results to quantitatively agree with theory in the former and qualitatively so in the latter, which suggest that the transition should be detectable in a wide array of numerical and experimental systems. Interestingly, although the Gardner transitions is primarily associated with structural glass formers, we also find features of the transition in crystals of polydisperse particles once the landscape becomes rough.   

Scaling theory for the jamming transition

The existence of a critical jamming transition, which marks the onset of rigidity in athermal packings of spheres, suggests that universal physics underlies the origin and nature of rigidity in disordered solids ranging from glasses to foams and granular materials. The jamming transition was originally proposed as a zero-temperature critical point in a non-equilibrium phase diagram in packing density and shear stress. Many studies have documented critical phenomena near the jamming transition, including power-law scaling, diverging length scales and scaling collapse, and theories have been developed to understand these phenomena. However, a number of confusing features have precluded a unified critical scaling analysis of the transition. Here we resolve these issues to present a scaling ansatz for the jamming critical point in terms of density and shear stress. The theory predicts new exponents that we verify with numerical simulations.   

Frustration by Shape-Designed Local Polymorphism: A Near-Equilibrium Colloidal Glass of Hard Kites

We study glass formation in uniform Brownian dispersions of hard colloidal polygonal platelets having the shape of 72-degree achiral kites, fabricated using optical stepper lithography. These kites are confined to a plane through roughness-controlled depletion attractions, and they diffuse in two-dimensions as we very slowly raise the particle density in the system. Although the densest packing of these kites is a crystalline lattice that fully tiles the plane, remarkably, we observe that the kites do not crystallize even for such quasi-static osmotic compression. By contrast, we have previously shown that such slow compression does cause crystallization of Brownian systems of other convex 2D lithographic shapes, such as squares and rhombs. Instead, the system of kites forms a disordered glass that undergoes an ergodic to non-ergodic transition, both in a rotational and a translational sense, while remaining near-equilibrium, as we measure by video particle tracking. We show that the high diversity of few-particle local polymorphic configurations (LPCs) of kites, related to our choice of angles and lengths in the designed shape, is responsible for suppressing long range spatial order and consequently favors glass formation instead. The prevalence and diversity of 5-particle LPCs, such as the pentagonal star, frustrate crystallization because these pentagonal LPCs are topologically different than the one 4-particle LPC that corresponds to the space-filling crystal. We anticipate that this mechanism of glass formation through shape-dependent frustration by diverse and incommensurate LPCs will also be relevant for molecular systems in three dimensions.   

Solution of the dynamcs of high-dimensional liquids

The dynamics of a liquid composed of particles with spherically symmetric potentials has been solved exactly in limit of high dimensions d. The calculation is long but straightforward. At high density, an ergodicity-breaking glass transition is found. This computation allows one to assess the validity of approximation schemes such as Mode-Coupling Theory. As a by-product, because our calculation is, if not rigorous, elementary, an improvement in the bound for sphere packings in large dimensions is now at hand.   

Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics

We revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. We focus on the spinodal of an Ising model in a quenched random field (RFIM), which has many applications in many areas from materials to social science. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the spinodal transition is due to the depinning and the subsequent expansion of rare droplets. We work out the critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild non-analyticities much like in a Griffith phenomenon. Thanks to the recently established connection between the spinodal of the RFIM and glassy dynamics, our results allow us to conclusively assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glass-forming liquids.