Distribution of domain sizes in the zero temperature Glauber dynamics of the one-dimensional Potts model

For the zero temperature Glauber dynamics of the q-state Ports model, we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one-species coagulation model (A+A-->A). In the long time limit, this distribution is universal and, from its (complicated) exact expression, we extract its behavior in various regimes. Our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently. Considering the dynamics of domain walls as a reaction-diffusion model A+A-->A with probability (q-2)/(q-1) and A+A-->phi with probability 1/(q-1), we calculate the pair correlation function in the long time regime.