Universal behavior in finite 2D kinetic ferromagnets

We show that quenching and coarsening of the kinetic Ising model with a non-conserved order parameter displays the same average evolution for finite systems of arbitrary size. This multiscale similarity applies not just within the characteristic length scale of the system, but also at all length and time scales, including in the regime where simple dynamical scaling fails for finite systems. As a consequence, beyond rapidly decaying finite size effects, the evolution of correlations in small systems exactly parallels arbitrarily larger cases. We suggest that dynamical scaling data collapse can be partially restored with an area law-like correction, but unlike the multiscale behavior, this does not hold for distances approaching a quarter of the system size