Jamming vs. Caging in Three Dimensional Jamming Percolation

TL;DR

This paper studies a 3D kinetically-constrained model revealing two distinct phase transitions: a mixed-order jamming transition and a continuous caging transition characterized by percolation theory.

Contribution

It introduces a model that differentiates between jamming and caging phenomena and characterizes the caging transition as a continuous percolation transition with known critical exponents.

Findings

Finite fraction of particles become frozen at jamming density

Caging transition is continuous and matches random percolation exponents

Distinct densities for jamming and caging transitions

Abstract

We investigate a three-dimensional kinetically-constrained model that exhibits two types of phase transitions at different densities. At the jamming density $ \rho_J $ there is a mixed-order phase transition in which a finite fraction of the particles become frozen, but the other particles may still diffuse throughout the system. At the caging density $ \rho_C > \rho_J $, the mobile particles are trapped in finite cages and no longer diffuse. The caging transition occurs due to a percolation transition of the unfrozen sites, and we numerically find that it is a continuous transition with the same critical exponents as random percolation.