00-164 N. Cancrini, F. Martinelli

Diffusive scaling of the spectral gap for the dilute Ising lattice gas dynamics below the percolation threshold (444K, postcript gzipped) 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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