Dynamic facilitation picture of a higher-order glass singularity

TL;DR

This paper demonstrates that facilitated spin models on Bethe lattices can reproduce higher-order glass singularities predicted by mode-coupling theory, showing different transition types depending on facilitation strength.

Contribution

It introduces a facilitated spin mixture model that captures higher-order glass transition singularities on Bethe lattices, aligning with MCT predictions.

Findings

Reproduction of higher-order singularities in facilitated spin models.

Transition types depend on facilitation strength, hybrid or continuous.

Results align with mode-coupling theory predictions.

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.