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We investigate a three-dimensional kinetically-constrained model thatexhibits two types of phase transitions at different densities. At the jammingdensity $ \rho_J $ there is a mixed-order phase transition in which a finitefraction of the particles become frozen, but the other particles may stilldiffuse throughout the system. At the caging density $ \rho_C > \rho_J $, themobile particles are trapped in finite cages and no longer diffuse. The cagingtransition occurs due to a percolation transition of the unfrozen sites, and wenumerically find that it is a continuous transition with the same criticalexponents as random percolation.

Jamming vs. Caging in Three Dimensional Jamming Percolation