3 research outputs found
Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics
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 . The temperature dependence of the
prefactor is derived exactly. At low temperature, where the static
correlation length is large, the mean square displacement grows as
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 . The temperature dependence of the prefactor is derived exactly,
using the Kardar-Parisi-Zhang theory. At low temperature, the displacement
variance grows as in the coarsening regime, again proportionally to
the mean square domain length.Comment: 22 pages, 8 figures. A few minor changes and update