One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition – like that of other statistical systems – is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finitedimensional effects could dramatically change what happens in physical dimensions, d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step towards describing dynamic facilitation in the framework of the mean-field theory of glasses.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers / Charbonneau, P.; Jin, Y.; Parisi, Giorgio; Zamponi, F.. - In: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. - ISSN 0027-8424. - 111:42(2014), pp. 15025-15030. [10.1073/pnas.1417182111]

Hopping and the Stokes-Einstein relation breakdown in simple glass formers

PARISI, Giorgio;Zamponi, F.
2014

Abstract

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition – like that of other statistical systems – is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finitedimensional effects could dramatically change what happens in physical dimensions, d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step towards describing dynamic facilitation in the framework of the mean-field theory of glasses.
2014
Glass transition; fluctuations; statistical mechanics
01 Pubblicazione su rivista::01a Articolo in rivista
Hopping and the Stokes-Einstein relation breakdown in simple glass formers / Charbonneau, P.; Jin, Y.; Parisi, Giorgio; Zamponi, F.. - In: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. - ISSN 0027-8424. - 111:42(2014), pp. 15025-15030. [10.1073/pnas.1417182111]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/970869
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