Comment on "Temperature-dependent orientational ordering on a spherical surface modeled with a lattice spin model"

In Sec. II of the named paper, the authors study the planar model on a regular two-dimensional (square or triangular) lattice and find evidence of an ordering transition at finite temperatures in both cases. It is shown that their findings do not agree with, and appear to ignore, a number of mathematical results, which have been known in the literature for some decades to date, and entail orientational disorder at all finite temperatures, as well as the existence of the Berezinski-Kosterlitz-Thouless transition.