From Large Scale Rearrangements to Mode Coupling Phenomenology

Andrea Montanari; Guilhem Semerjian

doi:10.1103/physrevlett.94.247201

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From Large Scale Rearrangements to Mode Coupling Phenomenology

Andrea Montanari·Guilhem Semerjian

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Abstract

We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the temperature. Focusing on the low temperature limit, we identify the large scale rearrangements responsible for the dynamical slowing-down near the transition. We are able to characterize exactly the dynamics near criticality by analyzing the statistical properties of such rearrangements. Our approach can be generalized to a large variety of glassy models on sparse random graphs, ranging from satisfiability to kinetically constrained models.

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Andrea Montanari, Guilhem Semerjian. 2005-05-12. From Large Scale Rearrangements to Mode Coupling Phenomenology. https://doi.org/10.1103/physrevlett.94.247201

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