Abstract
One 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.
Highlights
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
In order to understand how the Gardner transition emerges in the mean-field description of structural glasses, it is useful to revisit its original discovery in a class of mean-field spin glasses
A key step on this path aimed to confirm that a Gardner transition and the physics associated with the Gardner phase can be found in systems other than hard spheres
Summary
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. A coordinated effort to better understand the putative materials properties of this transition in real(istic) physical systems has since ensued 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. In glasses and other amorphous solids, by contrast, rigidity emerges from the appearance of a multitude of long-lived metastable states. These solids spontaneously break translational invariance, but only for a finite—albeit long—time. The breakdown of solidity happens at larger deformations, where the metastable glass state disappears entirely This perspective elaborates on this point from a variety of outlooks.
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