Jamming percolation in three dimensions
School of Mechanical Engineering, Tel Aviv University - Tel Aviv 69978, Israel
Received: 3 January 2014
Accepted: 28 March 2014
We introduce a three-dimensional model for jamming and glasses, 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.
PACS: 64.70.Q- – Theory and modeling of the glass transition / 64.60.ah – Percolation / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EPLA, 2014