Model of cluster growth and phase separation: Exact results in one dimension

We present exact results for a lattice model of cluster growth in one dimension. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the unstable-phase, –1, spins with probabilityp. For cluster coarsening at phase coexistence,p=0, the conventional structure-factor scaling applies. In this limit our model falls in the class of diffusion-limited reactions A+A inert. The +1 cluster size grows diffusively, t, and the two-point correlation function obeys scaling. However, forp > 0, i.e., for the dynamics of formation of stable phase from unstable phase, we find that structure-factor scaling breaks down; the length scale associated with the size of the growing +1 clusters reflects only the short-distance properties of the two-point correlations.On leave of absence from Department of Physics, Clarkson University, Potsdam, New York 13699-5820.