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

Abstract

In a recent paper [Phys. Rev. E 92, 012123 (2015)PLEEE81539-375510.1103/PhysRevE.92.012123], a modified d-dimensional Φ^{4} model was investigated that differs from the standard one in that the Φ^{4} term was replaced by a nonlocal one with a potential u(x-x^{'}) that depends on a parameter σ and decays exponentially as |x-x^{'}|→∞ on a scale |m|^{-1}<∞. 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. It is shown that these claims are unfounded and based on misjudgments and an ill-conceived renormalization-group calculation.