Journal
ANNUAL REVIEW OF CONDENSED MATTER PHYSICS, VOL 8
Volume 8, Issue -, Pages 265-288Publisher
ANNUAL REVIEWS
DOI: 10.1146/annurev-conmatphys-031016-025334
Keywords
dynamical transition; hard sphere; Gardner transition; mean-field theory; dimension dependence; marginal stability
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Funding
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1055586] Funding Source: National Science Foundation
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Despite decades of work, gaining a first-principles understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic glass-forming model in the mean-field limit of infinite spatial dimension. Numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner, and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.
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