Microscopic models of mode-coupling theory: the $F_{12}$ scenario

TL;DR

This paper demonstrates that mode-coupling theory for supercooled liquids can be microscopically realized using facilitated spin models, revealing two types of glass transitions linked to percolation phenomena and providing insights into dynamical arrest mechanisms.

Contribution

It introduces a microscopic facilitated spin model realization of the ${ m F}_{12}$ schematic mode-coupling theory, connecting dynamical transitions to percolation processes and geometrical structures.

Findings

Identification of continuous and discontinuous glass transition lines.

Critical decay exponents match MCT predictions.

Transitions correspond to bootstrap and standard percolation processes.

Abstract

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the ${\mathsf F}_{12}$ schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamic glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamic facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the ${\mathsf F}_{13}$ schematic model.