Polytype Kinetics and Quenching of Spin Chains with Competing Interactions using Trimer-flip Dynamics

TL;DR

This paper studies the non-equilibrium dynamics of a spin system with competing interactions after a zero-temperature quench, revealing metastable states with stretched exponential decay and mapping to exclusion processes.

Contribution

It introduces a model of spin kinetics with 3-spin flip dynamics relevant to polytype layer stacking, analyzing metastability and autocorrelation decay.

Findings

System gets arrested in metastable states with inhomogeneous regions.

Autocorrelation decays as a stretched exponential with exponent 1/3.

Mapping to simple exclusion process explains the decay behavior.

Abstract

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 $\tau_o$.