GRAIN-GROWTH FROM HOMOGENEOUS INITIAL CONDITIONS - ANOMALOUS GRAIN-GROWTH AND SPECIAL SCALING STATES

We used the large-Q Potts model on a two-dimensional lattice to study the evolution of the disordered cluster developed from a perfect hexag onal lattice with a single defect. The distribution functions were not stable, while the average area and the number of grains in the cluste r grew linearly in time. However, the grains at the boundary of the cl uster formed a well defined region which reached a special scaling sta te with time invariant distributions but no scale change, contrary to the result of Levitan [Boris Levitan, Phys. Rev. Lett. 72, 4057 (1994) ]. The rate of propagation of disorder is the same as the rate of grow th of the cluster. Abnormal grain growth can occur without anisotropy of surface energy. It requires only widely spaced, modest size differe nces in an initially homogeneous array of grains.