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Jamming transition and critical scaling in a three dimensional spiral model
Antina Ghosh [1] , Yair Shokef [1]
[1] Tel Aviv University
Jamming transition and critical scaling in a three dimensional spiral model
Antina Ghosh, Yair Shokef
Disordered systems like granular media, colloids or atomic liquids when compressed or rapidly cooled from an initial equilibrium liquid state undergoes a transition to an amorphous solid like phase at higher densities . Such glass / jamming transitions are characterized by the onset of slow dynamics, where molecular motion are locally constrained due to the presence of other neighbors leading to a very high relaxation times. One of the simplest finite dimensional representation of such dynamics is by kinetically constrained models [1-5] where a spin /particle is only allowed to flip or move when a certain constraint is satisfied locally by its nearest neighboring sites. Spiral model [4-7] is one of such class of model that is previously shown [5] to undergo an ideal glass-jamming transition at a occupation density rc < 1 in two dimension. In the present work we numerically study the culling dynamics [8] of spiral models in two as well as in three dimensions. The average cull time as obtained at different initial occupation density shows a sharp peak at a critical density rc < 1 in both cases, implying correlation over long length scales and presence of percolating clusters in the system. We find a different critical density rc ~ 0.35 in 3D which is lower than the critical density ~ 0.7 as predicted for two dimensional spiral model. We further perform system size analysis, obtain and compare the scaling exponents at the critical density in both the dimension.
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