Domain Statistics in Coarsening Systems
P.L.Krapivsky and E. Ben-Naim
We study the domain number and size distributions in the
one-dimensional Ising and $q$-state Potts models subject to
zero-temperature Glauber dynamics. The survival probability of a
domain, $S(t)\sim t^{-\psi}$, and an unreacted domain,
$Q_1(t)\sim t^{-\delta}$, are characterized by two independent
nonrtrivial exponents. For the Ising case, we find $\psi=0.126$ and
$\delta=1.27$ using numerical simulations. We develop an
independent interval approximation (IIA) that predicts the qualitative
behavior of the domain distribution and provides good estimates for
the exponents. Exact results for the domain distribution are also
obtained in several solvable cases.
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