Jamming Percolation and Glass Transitions in Lattice Models

TL;DR

This paper introduces lattice gas models with simple interactions but complex constrained dynamics, demonstrating a dynamical glass transition characterized by ergodicity breaking and diverging correlation lengths.

Contribution

It presents a new class of lattice models that exhibit glass-like transitions and jamming behavior, with rigorous proof of ergodicity breaking at a critical density.

Findings

Ergodicity is broken above a critical density rho_c.

Diverging correlation lengths and timescales occur near the transition.

Dynamic correlations show two-step relaxation similar to glass-formers.

Abstract

A new class of lattice gas models with trivial interactions but constrained dynamics are introduced. These 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 timescales diverge as exp[C(rho_c-rho)^(-mu)]. Dynamic correlations display two-step relaxation similar to glass-formers and jamming systems.