On random graphs and the statistical mechanics of granular matter
Abdus Salam International Centre for Theoretical Physics -
34100 Trieste, Italy
2 S. N. Bose National Centre for Basic Sciences, Block JD Sector III Salt Lake, Calcutta 700 098, India
Accepted: 3 October 2001
The dynamics of spins on a random graph with ferromagnetic three-spin interactions is used to model the compaction of granular matter under a series of taps. Taps are modelled as the random flipping of a small fraction of the spins followed by a quench at zero temperature. We find that the density approached during a logarithmically slow compaction -the random-close-packing density-corresponds to a dynamical phase transition. We discuss the role of cascades of successive spin-flips in this model and link them with density-noise power fluctuations observed in recent experiments.
PACS: 05.20.-y – Classical statistical mechanics / 45.70.Cc – Static sandpiles; granular compaction / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, 2001