  The dynamics of quasi-stationary states of long-range interacting systems
with $N$ particles can be described by kinetic equations such as the
Balescu-Lenard and Landau equations. In the case of one-dimensional homogeneous
systems, two-body contributions vanish as two-body collisions in one dimension
only exchange momentum and thus cannot change the one-particle distribution.
Using a Kac factor in the interparticle potential implies a scaling of the
dynamics proportional to $N^\delta$ with $\delta=1$ except for one-dimensional
homogeneous systems. For the latter different values for $\delta$ were reported
for a few models. Recently it was show by Rocha Filho and collaborators [Phys.\
Rev.\ E {\bf 90}, 032133 (2014)] for the Hamiltonian mean-field model that
$\delta=2$ provided that $N$ is sufficiently large, while small $N$ effects
lead to $\delta\approx1.7$. More recently Gupta and Mukamel [J.\ Stat.\ Mech.\
P03015 (2011)] introduced a classical spin model with an anisotropic
interaction with a scaling in the dynamics proportional to $N^{1.7}$ for a
homogeneous state. We show here that this model reduces to a one-dimensional
Hamiltonian system and that the scaling of the dynamics approaches $N^2$ with
increasing $N$. We also explain from theoretical consideration why usual
kinetic theory fails for small $N$ values, which ultimately is the origin of
non-integer exponents in the scaling.
