A minimal model for kinetic arrest

To elucidate slow dynamics in glassy materials, we introduce the {\it Figure-8 model} in which $N$ hard blocks undergo Brownian motion around a circuit in the shape of a figure-8. This system undergoes kinetic arrest at a critical packing fraction $\phi=\phi_g < 1$, and for $\phi\approx\phi_g$ long-time diffusion is controlled by rare, cooperative `junction-crossing' particle rearrangements. We find that the average time between junction crossings $\tau_{JC}$, and hence the structural relaxation time, does not simply scale with the configurational volume $\OmegaLow$ of transition states, because $\tau_{JC}$ also depends on the time to complete a junction crossing. The importance of these results in understanding cage-breaking dynamics in glassy systems is discussed.