Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2003-05

March 2003

A Second Threshold for the Hard-core Model on a Bethe Lattice

Graham R. Brightwell and Peter Winkler


We determine the approximate value of a critical activity for the hard-core model on the Bethe lattice, which determines whether the unique simple invariant Gibbs measure is extremal. This “recovery threshold” turns out to be different both from the threshold for unique Gibbs measure and (in contrast to the Ising model) from the threshold for recovery of root information purely from statistical information about distant sites.

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