Static and dynamic lengthscales in a simple glassy plaquette model

TL;DR

This paper investigates static and dynamic correlations in a 2D spin model with plaquette interactions, revealing glassy behavior, spatial heterogeneity, and diverging lengthscales akin to supercooled liquids and kinetically constrained models.

Contribution

It provides an analytic and simulation-based analysis of static and dynamic correlations in a simple glassy plaquette model, highlighting the role of effective kinetic constraints.

Findings

Dynamic heterogeneity with diverging lengthscales

Glass-like slow dynamics at low temperatures

Analogy with kinetically constrained models

Abstract

We study static and dynamic spatial correlations in a two-dimensional spin model with four-body plaquette interactions and standard Glauber dynamics by means of analytic arguments and Monte Carlo simulations. We study in detail the dynamical behaviour which becomes glassy at low temperatures due to the emergence of effective kinetic constraints in a dual representation where spins are mapped to plaquette variables. We study the interplay between non-trivial static correlations of the spins and the dynamic `four-point' correlations usually studied in the context of supercooled liquids. We show that slow dynamics is spatially heterogeneous due to the presence of diverging lengthscales and scaling, as is also found in kinetically constrained models. This analogy is illustrated by a comparative study of a froth model where the kinetic constraints are imposed.