  We discuss relaxation and aging processes in the one- and two-dimensional
$ABC$ models. In these driven diffusive systems of three particle types, biased
exchanges in one direction yield a coarsening process characterized in the long
time limit by a logarithmic growth of ordered domains that take the form of
stripes. From the time-dependent length, derived from the equal-time spatial
correlator, and from the mean displacement of individual particles different
regimes in the formation and growth of these domains can be identified.
Analysis of two-times correlation and response functions reveals dynamical
scaling in the asymptotic logarithmic growth regime as well as complicated
finite-time and finite-size effects in the early and intermediate time regimes.
