Stochastic Dynamics for the Dilute Ising Lattice Gas: Results and Open Problems

#### N. Cancrini, F. Martinelli

2001, v.7, Issue 1, 39-50

ABSTRACT

We review some results on the relaxation properties of non conservative and conservative stochastic lattice gas dynamics reversible with respect to the grand canonical and canonical Gibbs measure of the bond dilute Ising model on $Z^d$, respectively. In particular we show that in the conservative case and when the dilution is below the percolation threshold there is no dynamical phase transition when the inverse temperature crosses the critical value of the pure Ising model. We then comment on some interesting open problems in the subject.

Keywords: Kawasaki dynamics,random ferromagnet,spectral gap,equivalence of ensembles