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

Abstract

In a recent paper [Phys. Rev. E \textbf{92}, 012123 (2015)] a modified $d$-dimensional $\Phi^4$ model was investigated which differs from the standard one 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 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 $d_\sigma=4+2\sigma$. Performing a one-loop calculation they arrive at expansions in powers of $\epsilon_\sigma=d_\sigma-d$ for critical exponents such 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 claims are unfounded and based on misjudgments and an ill-conceived renormalization group calculation.