Issue
EPL
Volume 88, Number 1, October 2009
Article Number 16001
Number of page(s) 6
Section Condensed Matter: Structural, Mechanical and Thermal Properties
DOI http://dx.doi.org/10.1209/0295-5075/88/16001
Published online 16 October 2009
EPL, 88 (2009) 16001
DOI: 10.1209/0295-5075/88/16001

Mode coupling as a Landau theory of the glass transition

A. Andreanov1, G. Biroli2 and J.-P. Bouchaud3

1   Theoretical Physics, University of Oxford - 1 Keble Road, Oxford, OX1 3NP, UK, EU
2   Institut de Physique Théorique, CEA, IPhT and CNRS, URA 2306 - F-91191 Gif-sur-Yvette, France, EU
3   Science and Finance, Capital Fund Management - 6 Bd Haussmann, 75009 Paris, France, EU

a.andreanov1@physics.ox.ac.uk

received 26 March 2009; accepted in final form 16 September 2009; published October 2009
published online 16 October 2009

Abstract
We derive the Mode-Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher-order non-local corrections that modify the standard MCT equations, we find that the square-root singularity of the order parameter, the scaling function in the $\beta $ regime and the functional relation between the exponents defining the $\alpha $ and $\beta $ time scales are universal and left intact by these corrections.

PACS
64.70.Q- - Theory and modeling of the glass transition.
64.60.Ht - Dynamic critical phenomena.
64.60.F- - Equilibrium properties near critical points, critical exponents.

© EPLA 2009