In glasses and other amorphous solids, by contrast, rigidity emerges from the appearance of a multitude of long-lived metastable states. The resulting crystalline solid is “thermodynamically” stable. In (perfect) crystals, rigidity is due to the spontaneous breaking of translational invariance that follows a first-order phase transition. To understand what a Gardner transition might look like in a materials context, we need to recall that a hallmark of solids is their elastic response to small deformations, i.e., their rigidity. We also include an array of recent results that help identify upcoming research challenges. We here focus exclusively on Gardner physics but do so for a richer variety of glass formers and from a broader variety of viewpoints. In contrast to a recent review of hard sphere glasses, 1 the scope of this perspective is thus both narrower and broader.

This perspective aims to contextualize the many theoretical, numerical, and experimental opportunities that lie ahead. Because these advances have taken place fairly rapidly and over a range of subfields, it can be challenging to piece them together into a forward vision.

A coordinated effort to better understand the putative materials properties of this transition in real(istic) physical systems has since ensued. The recent surge in interest follows from the realization that mean-field models of structural glasses, which are exact in the limit of infinite dimension, d → ∞, can also undergo such a transition. Moreover, the anomalous temperature drop observed about 1 sec after the expansion marks the point at which convection currents sweep away the heated gas which has accumulated immediately adjacent to the thermocouple.As recently as five years ago, the Gardner transition was but an exotic feature of abstract models known only by a cabal of statistical physicists. The seemingly rapid response of the thermocouple is an indication of the attainment of the steady-state heat flow from the thermocouple and is not an indication that the thermocouple is reading the temperature of the ambient gas accurately. The measurements of Israel and Nix can be explained in terms of a thermal analysis of the thermocouple itself. An analysis of the heat and vapor diffusion from the walls of the chamber indicates that the counter does indeed develop the supersaturations predicted by thermodynamics in the absence of dropwise condensation and that the natural sensitive time is of the order of 0.3 sec. The measurement of the temperature drop in a dry Pollak condensation nucleus counter by Israel and Nix has been interpreted as an indication that the expansion process does not yield as high a supersaturation as predicted by thermodynamics.

Heated by J.C. Gardner