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

¹ 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

Received: 5 January 2004
Accepted: 30 April 2004

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 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.