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In a recent paper [Phys. Rev. E \textbf{92}, 012123 (2015)] a modified$d$-dimensional $\Phi^4$ model was investigated which differs from the standardone in that the $\Phi^4$ term was replaced by a nonlocal one with a potential$u(\bm{x}-\bm{x}')$ that depends on a parameter $\sigma$ and decaysexponentially as $|\bm{x}-\bm{x}'|\to\infty$ on a scale $|m|^{-1}<\infty$. Theauthors claim the upper critical dimension of this model to be$d_\sigma=4+2\sigma$. Performing a one-loop calculation they arrive atexpansions in powers of $\epsilon_\sigma=d_\sigma-d$ for critical exponentssuch as $\eta$ and related ones to $O(\epsilon_\sigma)$ whose$O(\epsilon_\sigma)$ coefficients depend on $\sigma$ and the ratio$w=m^2/\Lambda^2$, where $\Lambda$ is the UV cutoff. We show that these claimsare unfounded and based on misjudgments and an ill-conceived renormalizationgroup calculation.

Comment on "Nonlocal quartic interactions and universality classes in perovskite manganites"