For nearest-neighbour spin systems on subcritical dynamical percolation, sufficiently slow edge dynamics force mixing time Θ(λ^{-1} log N), with cutoff as λ→0.
Information percolation and cutoff for the stochastic Ising model.Journal of the American Mathematical Society, 29(3):729–774, Sep 2015
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Mixing times of spin systems on dynamical percolation
For nearest-neighbour spin systems on subcritical dynamical percolation, sufficiently slow edge dynamics force mixing time Θ(λ^{-1} log N), with cutoff as λ→0.