Jamming percolation and glassy dynamics

TL;DR

This paper analyzes the dynamical glass-jamming transition in Knight models, revealing a discontinuous percolation transition with unconventional features that lead to ergodicity breaking and glass-like relaxation dynamics.

Contribution

It introduces Knight models as finite-dimensional systems with an ideal glass-jamming transition driven by a unique percolation process.

Findings

Percolation transition is discontinuous with a compact cluster at the transition.

Divergence of cluster size faster than any power law as density approaches critical.

Relaxation times diverge similarly to the Vogel-Fulcher law.

Abstract

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we review some of our previous works on Kinetically Constrained Models. The Knights models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when $\rho\nearrow\rho_c$. These properties give rise for Knight models to an ergodicity breaking transition at $\rho_c$: at and above $\rho_{c}$ a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.