Jamming Percolation and Glass Transitions in Lattice Models

Abstract

A new class of lattice gas models with trivial interactions but constrained dynamics is introduced. These models are proven to exhibit a dynamical glass transition: above a critical density ${\rho }_c$ ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and time scales diverge as $\exp [C({\rho }_c-\rho {)}^{-\mu }]$. Dynamic correlations display two-step relaxation similar to glass formers and jamming systems.