Dynamical phase transitions in cluster growth processes where growth sites have a finite lifetime

Abstract

The authors discuss variants of the Eden model for cluster growth, where growth sites have a finite lifetime tau . Time is increased by 1/G when a growth site is transformed into a cluster site; G is the total number of growth sites present at that time. They find by Monte Carlo simulation that the growth process depends drastically on tau . Below a critical lifetime tau c ( tau c approximately=0.80 on the square lattice) the clusters are described by the fractal dimension of self-avoiding random walks, df=4/3, and the number of cluster sites s increases proportional to time t. Above tau c, one finds Eden clusters with df=2 and s approximately=t2. Finally, the authors extend results to inhomogeneous media (percolation systems) where a fraction (1-p) of sites is not accessible to the growth process, and discuss the phase diagram.