Recently an interesting phase transition scenario in the context of a planar Ising system with a grain boundary was revealed [Phys. Rev. Lett. 93, 076101 (2004)]]. In this paper we study in more detail the relaxation dynamics of this system and show how the grain boundary acts as a guide spatially confining matter transport. This is done by performing simulations using the continuous time Monte Carlo algorithm with Kawasaki dynamics. We also set up the problem as a solid-on-solid model and formulate corresponding Langevin equations for the dynamics in two cases, with and without matter conservation.
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Abraham et al. (2004) studied this question.
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