SELF-ORGANIZED CRITICALITY IN DYNAMICS WITHOUT BRANCHING

We demonstrate the phenomenon of self-organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant, i.e., a walker who can see only nearest neighbors. The ant acts on the underlying lattice aiming at uniform digging, i.e., reduction of the height profile of the surface but is unaffected by the underlying latt ice. In one, two, and three dimensions we have explored this model and have obtained power laws in the time intervals between consecutive ev ents of ''digging.'' Being a simple random walk, the power laws in spa ce translate to power laws in time. We also study the finite size scal ing of asymptotic scale invariant process as well as dynamic scaling i n this system. This model differs qualitatively from the cascade model s of SOC.