Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 109, Issue 35, Pages 13939-13943Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1211825109
Keywords
mean-field theory; van Hove function; non-ergodic parameter; non-Gaussian cage
Categories
Funding
- National Science Foundation [DMR-1055586]
- ERC [247328]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1055586] Funding Source: National Science Foundation
- European Research Council (ERC) [247328] Funding Source: European Research Council (ERC)
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The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed upon regarding why a fluid becomes sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension d, we find the cage to keep a nontrivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is qualitatively supported here and non-mean-field corrections are found to remain small on decreasing d, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.
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