Critical Phenomena in Glasses
Supercooled liquids become increasingly sluggish upon cooling down to the glass temperature Tg where they can no longer be studied in equilibrium on the laboratory scale and behave as off-equilibrium amorphous solids, i.e., glasses. Simple activated dynamics account for the behavior of so-called strong liquids, but deviations from Arrhenius behavior are observed in fragile ones and have defied explanation for decades. Technical advances in experiments have steadily unveiled more facets of the puzzling phenomenology of fragile liquids including notably two-step relaxation, stretched exponentials, superposition principles, and dynamical heterogeneities. Theoretical efforts have developed mainly around the idea that some sort of finite-temperature critical phenomenon is at play, the key role in the discussion being played by two different critical points. The first is thought to occur above Tg, and therefore it is not really a phase transition but rather a dynamical crossover. Numerical studies have shed much light on its nature, and nowadays it is largely believed to be the outcome of the smoothing of a sharp singularity spuriously predicted by mode-coupling theory. The existence of a dynamical crossover is largely accepted, and what is disputed is whether that is the end of the story.
Those who believe this is not the case typically put forward the classic hypothesis of a true thermodynamic phase transition to an amorphous glass state at some finite temperature below Tg. Originally suggested by elementary extrapolations of experimental data, this putative critical point is nowadays supposed to be a complex and fascinating object, notably the locus of a configurational entropy crisis accompanied by a divergent static correlation length. The quest to establish its existence, reinvigorated by the discovery of the glass/spin-glass analogy, is very much open but has produced nonetheless significant advances both at the theoretical and numerical level. Opponents of the thermodynamic transition scenario include notably those who advocate for dynamic facilitation, as realized in kinetically constrained models, to explain physics solely in terms of a dynamical crossover. Understanding dynamics between the crossover temperature and Tg would help assess both the range of validity of a description in terms of the crossover and whether something qualitatively different must be invoked close to Tg and below. Here the essential missing piece of information is the nature and spatial extent of the activated processes that should rule the dynamics: at the theoretical level, a consistent, beyond phenomenological, theory of these dynamical processes has still to be developed; at the experimental level, current techniques do not have enough spatial resolution; finally numerical simulations have been typically confined to higher temperatures due to hardware speed limitations but are beginning to access the crossover region and may provide some guidance in the coming years.
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