Temporally periodic phases and kinetic roughening

The analogy between temporally periodic phases of noisy extended driven systems and smooth interfaces in growth models is used to derive results for both problems, viz., stable, temporally quasiperiodic phases with long-range spatial order can in fact occur for noisy, short-range, isotropic rules in dimensions d>2. For d=2, temporally quasiperiodic phases have algebraic, rather than long-range order, and occur only in anisotropic systems. Anisotropic rules can also produce smooth, commensurately growing interfaces with d≥2 dimensions for generic parameter values.