Minimal model for kinetic arrest.

To elucidate slow dynamics in glassy materials, we introduce the 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 approximately 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 Omega c 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.