Spatial scaling in persistence

We discuss persistence in the context of non-equilibrium processes such as coarsening in Ising and Potts models. The persistence phenomenon shows strong spatial correlation with a correlation length ξ which diverges with time. In the correlated region r<ξ, persistent sites form a fractal and the structure evolves in time obeying a dynamical scaling. We discuss such fractal formation in the context of a reaction–diffusion system in one dimension.