COARSENING IN THE 1D ISING-MODEL EVOLVING WITH SWENDSEN-WANG DYNAMICS- AN UNUSUAL SCALING

We consider a simple model of domain growth: the zero-temperature 1D I sing model evolving according the Swendsen-Wang dynamics. We find that in the long-time limit, the pair correlation function scales with a c haracteristic length increasing as the square of the average domain si ze. In that limit, a few large domains occupy almost all the space wit h many small domains between them. In contrast to the usual picture of coarsening, the average domain size here is not a characteristic leng th of the growth problem. Instead, one finds a power-law distribution for the sizes of large domains with a cut-off at a length which grows as the square of the average size of the domains.