Dynamics of spreading phenomena in two-dimensional Ising models

We consider the time evolution of two Ising systems that differ at time t=0 in the orientation of only one spin. The detailed time development is calculated from two algorithms: (i) Glauber dynamics and (ii) Q2R dynamics (a deterministic cellular automaton). We find that for both algorithms spreading of ``damaged regions'' is greatly hindered below a threshold temperature ${\mathrm{T}}_{\mathrm{s}}$ (or energy), which agrees numerically with the Curie point. For Glauber dynamics ${\mathrm{T}}_{\mathrm{s}}$ is found to be a sharp phase transition point; for Q2R dynamics we find a kinetic slowing down which is reminiscent of a (spin-) glass transition.