Domain statistics in coarsening systems

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 $S\left(t\right)\mathrm{}\sim t^{-\psi }$ and an unreacted domain $Q_1\mathrm{}\left(t\right)\mathrm{}\sim t^{-\delta }$ are characterized by two independent nontrivial exponents. For the Ising case, we find $\psi =0.126\mathrm{}$ and $\delta =1.27\mathrm{}$ using numerical simulations. We develop an independent interval approximation 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.