Jamming in Hierarchical Networks

Abstract

We study the Biroli-Mezard model for lattice glasses on a number of hierarchical networks. These networks combine certain lattice-like features with a recursive structure that makes them suitable for exact renormalization group studies and provide an alternative to the mean-field approach. In our numerical simulations here, we first explore their equilibrium properties with the Wang-Landau algorithm. Then, we investigate their dynamical behavior using a grand-canonical annealing algorithm. We find that the dynamics readily falls out of equilibrium and jams in many of our networks with certain constraints on the neighborhood occupation imposed by the Biroli-Mezard model, even in cases where exact results indicate that no ideal glass transition exists. But while we find that time-scales for the jams diverge, our simulations cannot ascertain such a divergence for a packing fraction distinctly above random close packing. In cases where we allow hopping in our dynamical simulations, the jams on these networks generally disappear.

9 pages, several corrections. For related information, see http://www.physics.emory.edu/faculty/boettcher/

References in corpus (11)

• Theoretical perspective on the glass transition and amorphous materials
• The Jamming Transition in Granular Systems
• Fractal free energy landscapes in structural glasses
• Unified study of glass and jamming rheology in soft particle systems
• Dynamic criticality at the jamming transition
• Overlap fluctuations in glass-forming liquids
• A microscopic mean-field theory of the jamming transition
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Hierarchical, Regular Small-World Networks
• A Lattice Model for Colloidal Gels and Glasses
• Optimal Vertex Cover for the Small-World Hanoi Networks