Origin of steeper initial growth for CH coupling under columnar disorder

Ascertain the mechanism responsible for the steeper-than-expected initial roughness growth observed for the cosine coupling with higher-order terms (CH) in a one-dimensional ring of phase oscillators with columnar disorder, prior to the crossover into columnar KPZ scaling.

Background

Under columnar disorder, non-odd coupling functions typically display columnar KPZ scaling, while odd-symmetric functions exhibit columnar Edwards–Wilkinson scaling. For the CH coupling, the authors observe an initial growth regime that is even steeper than the subsequent KPZ-like behavior.

They explicitly state that the origin of this steep initial regime is unclear, identifying the need to explain the transient scaling preceding the established columnar KPZ regime.