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Analytic determination of dynamical and mosaic length scales in a Kac glass model

Silvio Franz·Andrea Montanari
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Abstract

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.

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Silvio Franz, Andrea Montanari. 2007-04-16. Analytic determination of dynamical and mosaic length scales in a Kac glass model. https://doi.org/10.1088/1751-8113%2F40%2F11%2Ff01

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