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Keyword: hard-core model ×Clear all

2 claims from 1 paper

1. Physics and Astronomy › Theoretical and Computational Physics

   The hard-core model on random graphs revisited

   Barbier, Krząkała, Zdeborová and Zhang · Journal of Physics Conference Series · 2013

   The paper revisits the hard-core (independent set) model on random graphs with the cavity method, aiming to reconcile the small-degree and very-large-degree cases.

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   1. UncheckedUsing the cavity method, the authors give a closed-form conjecture for the densest packing on random regular graphs of degree 20 or more.“We revisit results that can be obtained using the (heuristic) cavity method and show that it provides a closed-form conjecture for the exact density of the densest packing on random regular graphs with degree K>=20, and that for K>16 the nature of the phase transition is the same as for large K.”
   2. UncheckedThe paper states that the hard-core model on random graphs is the simplest mean-field lattice model for structural glasses and jamming.“This also shows that the hard-code model is the simplest mean-field lattice model for structural glasses and jamming.”