Glass Transition in a 2D Lattice Model

TL;DR

This study models the compaction dynamics of cross-shaped particles on a 2D lattice, revealing a glassy phase with a stable amorphous packing density lower than maximum possible, relevant to biological membrane experiments.

Contribution

It introduces a lattice model for particle compaction that demonstrates a stable glassy phase with a specific limiting density, distinct from crystalline arrangements.

Findings

Filling process terminates at a glassy phase with density 0.171626.

Long-term filling rate vanishes as the square of density difference.

Particles form an amorphous, non-crystalline phase throughout the process.

Abstract

The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with a limiting coverage density \rho_{rcp}=0.171626(3), lower than the density of closest packing \rho_{cp}=0.2, and the long time filling rate vanishes like (\rho_{rcp}-\rho(t))^2. For the entire density regime the particles form an amorphous phase, devoid of any crystalline order. Therefore, the model supports a stable random packing state, as opposed to the hard disks system. Our results may be relevant to recent experiments studying the clustering of proteins on bilayer lipid membranes.