The convergence of the biased annihilating branching process and the double-flipping process in d

It is shown that, if the initial measure is translation-invariant, then finite-range stochastic Ising models allowing zero flip-rates converge. In particular, the biased annihilating process converges to a mixture of a product measure and [delta]ø and the double-flipping process converges to a product measure. The method of relative entropy is employed.