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

Giulio Biroli·Jean-Philippe Bouchaud
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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.

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Giulio Biroli, Jean-Philippe Bouchaud. 2004-05-03. Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition. https://doi.org/10.1209/epl%2Fi2004-10044-6

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