  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 the role of cascades of successive spin-flips in
this model and link them with density-noise power fluctuations observed in
recent experiments.
