  We consider the effects of a quench to T = 0 on a spin system with axial
next-next nearest neighbour Ising interactions, evolving under a conserved
3-spin flip dynamics. Such a model is motivated by the kinetics of stacking
layers in polytypes near the 3C-6H transition. We find that the system
generically gets arrested in interesting metastable states which have
inhomogeneously distributed quiescent and active regions. In such arrested
states, the autocorrelation function decays as a stretched exponential $\sim
\exp(-(t/\tau_{o})^{1 \over 3})$. The latter feature can be understood in terms
of a mapping of the dynamics within active stretches to the well known simple
exclusion process of particles on a line, and bounds can be put on $\tau_o$.
