Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model

Abstract

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 a power law $r(q,t)\sim t^{-\theta (q)}$ with a non-trivial dependence of the exponent $\theta (q)$ on $q$ and on space dimension. By mapping the problem on an exactly soluble one-species coagulation model ($A+A\to A$), we obtain the exact expression of $\theta (q)$ in dimension one.

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