EXACT FIRST-PASSAGE EXPONENTS OF 1D DOMAIN GROWTH - RELATION TO A REACTION-DIFFUSION MODEL

In the zero temperature Glauber dynamics of the ferromagnetic Ising or q-state Potts model, the size of domains is known to grow like t(1/2). Recent simulations have shown that the fraction r(q, t) of spins, which have never flipped up to time t, decays like the power law r(q, t) similar to t(-theta(q)) with a nontrivial dependence of the exponent theta(q) on q and on space dimension. By mapping the problem on an exactly soluble one-species coagulation model (A + A --> A), we obtain the exact expression of theta(q) in dimension one.