Chapter

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

Silvio Franz and Guilhem Semerjian

in Dynamical Heterogeneities in Glasses, Colloids, and Granular Media

Published in print July 2011 | ISBN: 9780199691470
Published online September 2011 | e-ISBN: 9780191729799 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199691470.003.0012

Series: International Series of Monographs on Physics

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

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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.

Keywords: glass transition; dynamical heterogeneity; analytical result; point-to-set correlation function

Chapter.  23619 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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