  We investigate the dynamics of two-dimensional site-diluted Ising
antiferromagnets. In an external magnetic field these highly disordered
magnetic systems have a domain structure which consists of fractal domains with
sizes on a broad range of length scales. We focus on the dynamics of these
systems during the relaxation from a long-range ordered initial state to the
disordered fractal-domain state after applying an external magnetic field. The
equilibrium state with applied field consists of fractal domains with a size
distribution which follows a power law with an exponential cut-off. The
dynamics of the system can be understood as a growth process of this
fractal-domain state in such a way that the equilibrium distribution of domains
develops during time. Following these ideas quantitatively we derive a simple
description of the time dependence of the order parameter. The agreement with
simulations is excellent.
