对“钙钛矿锰氧化物中的非定域四次相互作用和普适类”一文的评论
Comment on "Nonlocal quartic interactions and universality classes in perovskite manganites"
摘要：
在最近的一篇论文[Phys. Rev. E \textbf{92}，012123（2015）]中，研究了一种改进的$d$维$Φ^4$模型，其与标准模型的不同之处在于，$Φ^4$项被具有势$u(\bm{x}-\bm{x}')$的非局部项取代，该势$u(\bm{x}-\bm{x}')$取决于参数$σ$，并在尺度$|m|^{-1}<\infty$上以$|\bm{x}-\bm{x}'|\to\infty$的形式指数衰减。作者认为该模型的上临界维数为$d_σ=4+2σ$。执行一个循环计算，它们得到临界指数的$ε_σ=d_σ-d$幂的展开式，例如$η$和$O(ε_σ)$的相关指数，其$O(ε_σ)$系数取决于$σ$和比率$w=m^2/Λ^2$，其中$Λ$是UV截止。我们表明，这些说法是没有根据的，基于误判和一个构思不良的重整化群计算。
英文摘要：
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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