Pm. Gade et Mp. Joy, SELF-ORGANIZED CRITICALITY IN DYNAMICS WITHOUT BRANCHING, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 57(5), 1998, pp. 5019-5022
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.