Kinetics of domain growth in systems with local barriers

We study domain growth in spin-1 lattice models having nonconserved spin-flip kinetics with local barriers. Our primary motivation is to model the relaxational behavior of physical systems in which molecular motion is impeded by local kinetic barriers. The kinetic constraint is such that a spin from an up (down) state can flip to a down (up) state only via the zero state, which has a higher energy. We examine how the usual curvature-driven domain growth is affected by these local barriers, and whether the single-spin barriers have a collective effect. This paper presents comprehensive numerical results for phase ordering dynamics in this model using Monte Carlo simulations. We demonstrate dynamical scaling for domain-size distribution functions and spatial correlation functions. We also present results for the time dependence of characteristic length scales and autocorrelation functions. The length-scale behavior is interpreted in terms of the random walk of steps on domain boundaries. Furthermore, we present a simple stochastic model to derive an analytic expression for the autocorrelation function, which exhibits a stretched-exponential behavior over an extended regime—in agreement with our numerical simulations.