Spreading of damage in the ballistic deposition and larger curvature models.

Abstract

The damage spreading of various growth models is described. The damage spreading distance D of an initial small perturbation grows as ${\mathit{t}}^{\ensuremath{\gamma}}$ with time t. In the ballistic deposition model and the restricted solid-on-solid growth model \ensuremath{\gamma} is consistent with 1/z implying that D is proportional to the parallel correlation length obtained from the usual surface scaling where z is the dynamic critical exponent. The survival probability of an initial perturbation decays with a power law as a function of time. For the larger curvature model, however, the damage spreading distance grows much faster than the parallel correlation length. Possible implications of the damage spreading idea to the Family model are discussed. \textcopyright{} 1996 The American Physical Society.