Volume 67, Number 1, July 2004
|21 - 27
|01 June 2004
Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
Service de Physique Théorique Centre d'études de Saclay Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
2 Service de Physique de l'État Condensé, Centre d'études de Saclay Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
Accepted: 30 April 2004
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 ν 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 , as suggested by different forms of the Ginzburg criterion.
PACS: 05.70.Jk – Critical point phenomena / 64.60.Ht – Dynamic critical phenomena / 64.70.Pf – Glass transitions
© EDP Sciences, 2004
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