We investigate the motion of a tagged spin in a ferromagnetic Ising chain
evolving under Kawasaki dynamics. At equilibrium, the displacement is Gaussian,
with a variance growing as At1/2. The temperature dependence of the
prefactor A is derived exactly. At low temperature, where the static
correlation length ξ is large, the mean square displacement grows as
(t/ξ2)2/3 in the coarsening regime, i.e., as a finite fraction of the
mean square domain length. The case of totally asymmetric dynamics, where (+)
(resp. (−)) spins move only to the right (resp. to the left), is also
considered. In the steady state, the displacement variance grows as Bt2/3. The temperature dependence of the prefactor B is derived exactly,
using the Kardar-Parisi-Zhang theory. At low temperature, the displacement
variance grows as t/ξ2 in the coarsening regime, again proportionally to
the mean square domain length.Comment: 22 pages, 8 figures. A few minor changes and update