Distribution of domain sizes in the zero temperature Glauber dynamics of the 1 D Potts model

Abstract

For the zero temperature Glauber dynamics of the $q$-state Potts model, we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one-species coagulation model ($A+A\to A$). 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 $A+A\to A$ with probability $(q-2)/(q-1)$ and $A+A\to \varnothing$ with probability $1/(q-1)$, we calculate the pair correlation function in the long time regime.

LaTeX 24 pages. 2 postscript figures. Submitted to PRE 15-april-96

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