Jamming Percolation in Three Dimensions

We introduce a three-dimensional kinetically-constrained model for jamming and glasses [1], and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and glass-transitions, this is a mixed-order transition; the discontinuity is accompanied by diverging length- and time-scales. Because one-dimensional directed-percolation paths comprise the backbone of frozen particles, the unfrozen rattlers may use the third dimension to travel between their cages. Thus the dynamics are diffusive on long-times even above the critical density for jamming. Our new model is a non-trivial extension of the two-dimensional spiral model [2]. \\[4pt] [1] A. Ghosh, E. Teomy, and Y. Shokef, \textit{Europhys. Lett.} \textbf{106}, 16003 (2014).\\[0pt] [2] G. Biroli and C. Toninelli, \textit{Eur. Phys. J. B} \textbf{64}, 567 (2008).