Dynamic facilitation picture of a higher-order glass singularity

Abstract

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a hybrid glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions.

4 pages, 3 figures; minor changes

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• Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
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• A note on weakly discontinuous dynamical transitions
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• Logarithmic critical slowing down in complex systems: from statics to dynamics