Caging and mosaic lengthscales in plaquette spin models of glasses

TL;DR

This paper analyzes plaquette spin models of glasses, revealing that static and dynamic lengthscales align with mosaic theory predictions, but nucleation arguments need refinement to accurately relate freezing lengths to relaxation times.

Contribution

It demonstrates that simple plaquette spin models exhibit glassy mosaic states and connects static lengthscales with dynamic correlations, highlighting limitations of traditional nucleation arguments.

Findings

Freezing lengthscales from statics match dynamic correlation lengths.

Mosaic approach's nucleation arguments do not fully explain relaxation times.

Models show glassy states without static singularities.

Abstract

We consider two systems of Ising spins with plaquette interactions. They are simple models of glasses which have dual representations as kinetically constrained systems. These models allow an explicit analysis using the mosaic, or entropic droplet, approach of the random first-order transition theory of the glass transition. We show that the low temperature states of these systems resemble glassy mosaic states, despite the fact that excitations are localized and that there are no static singularities. By means of finite size thermodynamics we study a generalised caging effect whereby the system is frozen on short lengthscales, but free at larger lengthscales. We find that the freezing lengthscales obtained from statics coincide with those relevant to dynamic correlations, as expected in the mosaic view. The simple nucleation arguments of the mosaic approach, however, do not give the correct relation between freezing lengths and relaxation times, as they do not capture the transition states for relaxation. We discuss how these results make a connection between the mosaic and the dynamic facilitation views of glass formers.