Abstract.
We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on ℤd at inverse temperature β. When the bond dilution density p is below the percolation threshold we prove that for any particle density and any β, with probability one, the spectral gap of the generator of the dyamics in a box of side L centered at the origin scales like L −2. Such an estimate is then used to prove a decay to equilibrium for local functions of the form where ε is positive and arbitrarily small and α = ½ for d = 1, α=1 for d≥2. In particular our result shows that, contrary to what happes for the Glauber dynamics, there is no dynamical phase transition when β crosses the critical value β c of the pure system.
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Received: 10 April 2000 / Revised version: 23 October 2000 / Published online: 5 June 2001
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Cancrini, N., Martinelli, F. Diffusive scaling of the spectral gap for the dilute Ising lattice-gas dynamics below the percolation threshold. Probab Theory Relat Fields 120, 497–534 (2001). https://doi.org/10.1007/PL00008790
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DOI: https://doi.org/10.1007/PL00008790