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

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

2006-06-05

arxiv.org/abs/cond-mat/0606113v3

J. Phys. A: Math. Theor. 40 No 11 (16 March 2007) F251-F257

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 eps figures. New version conform to the published one

Scientific paper

10.1088/1751-8113/40/11/F01

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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