Crossover from $\beta$- to $\alpha$-relaxation in cooperative facilitation dynamics

TL;DR

This paper demonstrates that the crossover from $eta$- to $ ext{alpha}$-relaxation in glassy systems can be quantitatively described by mode-coupling theory within the cooperative facilitation scenario, revealing universality and a dynamic realization of MCT.

Contribution

It shows that the crossover scaling in cooperative facilitation dynamics aligns with MCT predictions without adjustable parameters, highlighting universality and a dynamic realization of MCT.

Findings

Quantitative agreement with MCT predictions for relaxation crossover

Establishment of universality between MCT and CFS

Identification of a dynamic realization of MCT separate from RFOT scenario

Abstract

$\beta$ and $\alpha$ relaxation processes are dynamical scaling regimes of glassy systems occurring on two separate time scales which both diverge as the glass state is approached. We study here the crossover scaling from $\beta$- to $\alpha$- relaxation in the cooperative facilitation scenario (CFS) and show that it is quantitatively described, with no adjustable parameter, by the leading order asymptotic formulas for scaling predicted by the mode-coupling theory (MCT). These results establish: (i) the mutual universality of the MCT and CFS, and (ii) the existence of a purely dynamic realization of MCT which is distinct from the well established random-first order transition scenario for disordered systems. Some implications of the emerging kinetic-static duality are discussed.