  We consider zero-temperature, stochastic Ising models with nearest-neighbor
interactions in two and three dimensions. Using both symmetric and asymmetric
initial configurations, we study the evolution of the system with time. We
examine the issue of convergence of the dynamics and discuss the nature of the
final state of the system. By determining a relation between the median number
of spin flips per site, the probability p that a spin in the initial spin
configuration takes the value +1, and lattice size, we conclude that in two and
three dimensions, the system converges to a frozen (but not necessarily
uniform) state when p is not equal to 1/2. Results for p=1/2 in three
dimensions are consistent with the conjecture that the system does not evolve
towards a fully frozen limiting state. Our simulations also uncover `striped'
and `blinker' states first discussed by Spirin et al., and their statistical
properties are investigated.
