Domain growth dynamics is studied. We show that an exponent of a power-like time domain growth is determined not only by the conservation or nonconservation of the order parameter, but also by the asymmetry of single particle jumps. Domains that have an anisotropic pattern, such as (2X1), have a tendency to grow faster in certain direction than they do in others. The rate of expansion in different directions depends on the barriers for single particle jumps. As a result, dynamical behavior of systems which start in the same configurations and eventually reach the same equilibrium states is completely different. We show how differences in microscopic dynamics in a one dimensional Potts model lead to different rates of domain growth.

We observe a similar effect for a two-dimensional (2X1) ordering by changing the way in which a barrier for a jump depends on the number of neighboring particles. We show examples of the domain power growth which are characterized by different exponents.

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