Analytical approaches to time and length scales in models of glasses

Details Analytical approaches to time and length scales in models of glasses Analytical approaches to time and length scales in models of glasses

2010-09-27

arxiv.org/abs/1009.5248v1

Physics

Condensed Matter

Statistical Mechanics

Chapter of "Dynamical heterogeneities in glasses, colloids, and granular media", Eds.: L. Berthier, G. Biroli, J-P Bouchaud, L

Scientific paper

The goal of this chapter is to review recent analytical results about the growth of a (static) correlation length in glassy systems, and the connection that can be made between this length scale and the equilibrium correlation time of its dynamics. The definition of such a length scale is first given in a generic setting, including finite-dimensional models, along with rigorous bounds linking it to the correlation time. We then present some particular cases (finite connectivity mean-field models, and Kac limit of finite dimensional systems) where this length can be actually computed.

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