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 $u(\mathbf{x}-{\mathbf{x}}^{\prime })$ that depends on a parameter $\sigma$ and decays exponentially as $|\mathbf{x}-{\mathbf{x}}^{\prime }|\to \infty$ 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.

pdf-Latex, 2 pages, published extended version. The extension are reactions to claims and requests by the authors and the referee

References in corpus (1)

• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions