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

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

2004-01-15

arxiv.org/abs/cond-mat/0401260v2

Europhys. Lett. Vol 67 (2004) 21.

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1209/epl/i2004-10044-6

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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