# Rigorous Inequalities Between Length and Time Scales in Glassy Systems

@article{Montanari2006RigorousIB, title={Rigorous Inequalities Between Length and Time Scales in Glassy Systems}, author={Andrea Montanari and Guilhem Semerjian}, journal={Journal of Statistical Physics}, year={2006}, volume={125}, pages={23-54} }

Glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order. It is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length. We prove rigorous bounds between length and time scales implying the growth of a properly defined length when the relaxation time increases. Our results are valid in a rather general setting, which covers finite-dimensional and mean field systems.As an…

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