Phase-ordering and persistence: relative effects of space-discretization, chaos, and anisotropy

The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (Lemaı̂tre, Chaté, Phys. Rev. Lett. 82 (1999) 1140) are revisited with the help of detailed investigations of interface motion. It is shown that “normal”, curvature-driven-like domain growth is recovered at larger scales than considered before, and that the persistence exponent seems to be universal. Using generalized persistence spectra, the properties of interface motion in this deterministic, chaotic, lattice system are found to “interpolate” between those of the two canonical reference systems, the (probabilistic) Ising model, and the (deterministic), space-continuous, time-dependent Ginzburg–Landau equation.