Simulation of large Eden clusters

Abstract

Simulations of Eden clusters with more than ${10}^9$ sites by the use of a Cray Research Cray-2 supercomputer show that the thickness of the surface layer of round two-dimensional clusters, averaged over all directions, increases as the radius for sizes above 50?0?0 sites. In simulations of flat surfaces, on the other hand, the thickness increases as the square root of the height for strip widths above 500. The initial growth of such strips is not described by one single power law and asymptotically has a ‘‘dynamic’’ exponent close to (3/2), i.e., it increases as predicted theoretically with (height${)}^{1/3}$. In the range covered, our three-dimensional flat-surface thickness is not consistent with a logarithmic law, and also in four dimensions the thickness does not approach a constant. Round clusters with more than ${10}^9$ sites on the square lattice confirm the expected behavior due to anisotropy. Higher dimensions up to d=12 were also studied.