Comment on "Effect of long-range interactions on the critical behavior of the continuous Ising model"

Available mathematical results entail the absence of a proper ordering transition taking place at finite temperature in the case d = 1, sigma = 1.1, where the authors of the article commented on Rnd evidence of such a transition. Moreover, in contrast to the findings of the authors of the article, the case d = 2, sigma = 0 entails a ground-state energy per particle diverging logarithmically with increasing sample size, hence an infinite transition temperature.