Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition

Abstract

We show that the glass transition predicted by the Mode-Coupling Theory (MCT) is a critical phenomenon with a diverging length and time scale associated to the cooperativity of the dynamics. We obtain the scaling exponents nu and z that relate space and time scales to the distance from criticality, as well as the scaling form of the critical four-point correlation function. However, both these predictions and other well known MCT results are mean-field in nature and are thus expected to change below the upper critical dimension dc=6, as suggested by different forms of the Ginzburg criterion.

7 pages, 2 figures. Final version accepted on Europhysics Letters

References in corpus (7)

• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Theory of nonlinear rheology and yielding of dense colloidal suspensions
• Time and length scales in supercooled liquids
• Dynamic criticality in glass-forming liquids
• Barrier Softening near the onset of Non-Activated Transport in Supercooled Liquids: Implications for Establishing Detailed Connection between Thermodynamic and Kinetic Anomalies in Supercooled Liquids
• Spatially heterogeneous ages in glassy dynamics
• A Molecular Hydrodynamic Theory of Supercooled Liquids and Colloidal Suspensions under Shear

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