 00164 N. Cancrini, F. Martinelli
 Diffusive scaling of the spectral gap for the dilute Ising lattice
gas dynamics below the percolation threshold
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Apr 5, 00

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Abstract. We consider a conservative stochastic lattice gas
dynamics reversible with respect to the canonical Gibbs measure of the
bond dilute Ising model on $\Z^d$ at inverse temperature $\beta$. When the
bond dilution density $p$ is below the percolation threshold we prove
that for any particle density and any $\beta$, with probability one, the
spectral gap of the generator of the dynamics 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
${1\over t^{\a \epsilon}}$ where $\epsilon$ is positive and arbitrarily small and
$\alpha = {1\over 2}$ for $d=1$, $\a=1$ for $d\geq 2$. In particular our result
shows that, contrary to what happens for the Glauber dynamics, there is
no dynamical phase transition when $\beta$ crosses the critical value
$\beta_c$ of the pure system
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