Polytype kinetics and quenching of spin chains with competing interactions using trimer-flip dynamics

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 ∼exp(−(t/τo)13). 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 τo.