Geometric and healing laws in simple stochastic models of fracture in a sputtering process

We investigated two simple models of two-dimensional square lattice fracture under sputtering process conditions extending a previously studied model by Ausloos and Kowalski [Phys. Rev. B 45, 12 830 (1992)]. The models differ by the particle displacement rules during the fracture. Healing of the medium is observed in both models. This effect implies the formation of several thresholds during sputtering process fracture. They are distributed as a size-dependent power law. An avalanche like exponent is also obtained. We study this phenomenology within scaling arguments of classical percolation theory and mean-field arguments.