Surface structure and anisotropy of Eden clusters

Abstract

The simple Eden model is simulated with clusters which are orders of magnitude larger than those of some previous work. The 'surface' (perimeter) is slightly anisotropic and feels the underlying structure of the square lattice even for 17 million cluster sites. The width of the surface layer increases with increasing cluster mass, with an effective exponent presumably larger than 1/4 for averages over the whole circumference, and perhaps equal to 1/4 for flat surfaces. Width averages over a small angle are compared with the recent prediction of Plischke and Racz (1985). Even 17 million sites are not enough to see directly the asymptotic behaviour.