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

In a recent paper [Phys. Rev. E \textbf{92}, 012123 (2015)] a modified $d$-dimensional $Φ^4$ model was investigated which differs from the standard one in that the $Φ^4$ term was replaced by a nonlocal one with a potential $u(\bm{x}-\bm{x}')$ that depends on a parameter $σ$ and decays exponentially as $|\bm{x}-\bm{x}'|\to\infty$ on a scale $|m|^{-1}<\infty$. The authors claim the upper critical dimension of this model to be $d_σ=4+2σ$. Performing a one-loop calculation they arrive at expansions in powers of $ε_σ=d_σ-d$ for critical exponents such as $η$ and related ones to $O(ε_σ)$ whose $O(ε_σ)$ coefficients depend on $σ$ and the ratio $w=m^2/Λ^2$, where $Λ$ is the UV cutoff. We show that these claims are unfounded and based on misjudgments and an ill-conceived renormalization group calculation.

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