  Until very recently, the asymptotic occurrence of intrinsic anomalous scaling
has been expected to require concomitant effects for kinetically rough
interfaces, like quenched disorder or morphological instabilities. However,
counterexamples have been recently reported for simpler situations dominated by
time-dependent noise, as in the discrete growth system associated with an Ising
model proposed by H.\ Dashti-Naserabadi {\em et al.}\ [Phys.\ Rev.\ E {\bf
100}, 060101(R) (2019)], who assessed the equilibrium behavior of the model.
Here we revisit this system to characterize its time-dependent behavior in two
and three dimensions (one-and two-dimensional interfaces, respectively). While
the 3D case seems dominated by a fast evolution beyond critical dynamics, in
the 2D case numerical simulations of an associated time-dependent
Ginzburg-Landau equation retrieve the same static (roughness) exponents and the
same intrinsic anomalous scaling Ansatz as in the equilibrium case, throughout
the full time evolution. However, the dynamic exponent is seen to cross over
between two different values, none of which enables identification with
previously known universality classes of kinetic roughening. Simulations for
larger system sizes moreover suggest breakdown of scaling behavior at the
largest scales, suggesting that the previously reported scaling behavior may be
effective and restricted to relatively small systems.
