Structure and the Failure of the Linear Theory of Continuous Ordering

We present the results of numerical investigations of Ising models undergoing continuous ordering which indicate, for systems with large but finite interaction range R, that the time interval during which the linear theory of Cahn, Hilliard, and Cook fits the simulation data depends strongly on the length scale of observation. We associate the initial linear theory deviation at small length scales with the appearance of isolated structures or domains which form after a quench into the unstable region of thermodynamic space. These domains cannot be described by a linear theory; this implies, in contrast to earlier results, that the linear theory "breakdown" cannot be obtained by investigation of the linear itself for inconsistencies.