Domain growth in a one-dimensional driven diffusive system

The low-temperature coarsening dynamics of a one-dimensional Ising model, with conserved magnetization and subject to a small external driving force, is studied analytically in the limit where the volume fraction mu of the minority phase is small, and numerically for general mu. The mean domain size L(t) grows as t(1/2) in all cases, and the domain-size distribution for domains of one sign is very well described by the form P-l(l) alpha(l/L(3)exp[-lambda(mu)(l(2)/L(2))], which is exact for small mu (and possibly for all mu). The persistence exponent for the minority phase has the value 3/2 for mu --> 0.