Relaxation to equilibrium for two

We consider Glauber{type dynamics for two dimensional disordered magnets of Ising type. We prove that, if in equilibrium the disorder{averaged innuence of the boundary condition is suuciently small, then the corresponding Glauber dynamics is ergodic with probability one and the disorder{averaged of time{autocorrelations decays like e ?m(log t) 2. For the standard dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values 0 or J > 0, our results apply even if the active bonds percolate and J is larger than the critical value for the corresponding pure Ising model. For this model we also rigorously prove the existence of a dynamical phase transition when J crosses the critical value J c for the standard two dimensional Ising model.