对钙钛矿锰氧化物中非定域四次相互作用和普适类评论的答复
Reply to Comment on Nonlocal quartic interactions and universality classes in perovskite manganites
摘要：
注释[arXiv：cond-mat.stat.mech.，1602.02087v1（2016）]提出了一些问题，声称[Phys. Rev. E 92，012123（2015）]中提出的非定域模型哈密顿量等价于标准（短程）Φ^4理论。这些主张是基于相互作用顶点的低动量展开，不能应用于包含低动量和高动量的环积分内的顶点因子。在详细阐述重整化群计算中采用的动量壳抽取方案的重要步骤之后，我们明确地指出了决定自能和顶点函数的环积分的内（高）动量和外（低）动量的相互作用，从而产生了不同于标准（短程）Φ^4理论的修正（对裸参数）。采用明确的数学参数，我们表明，这种差异仍然存在时，相互作用的范围被假定为长（短）范围内的晶格常数（相关长度），产生的临界指数，在原来的文件。
英文摘要：
Comment [arXiv:cond-mat.stat.mech., 1602.02087v1 (2016)] has raised questions claiming that the nonlocal model Hamiltonian presented in [Phys. Rev. E 92, 012123 (2015)] is equivalent to the standard (short-ranged) Φ^4 theory. These claims are based on a low momentum expansion of the interaction vertex that cannot be applied to the vertex factors containing both low and high momenta inside the loop-integrals. Elaborating upon the important steps of the momentum shell decimation scheme, employed in the renormalization-group calculation, we explicitly show the interplay of internal (high) and external (low) momenta determining the loop integrals for self-energy and vertex functions giving rise to corrections (to the bare parameters) different from those of the standard (short-ranged) Φ^4 theory. Employing explicit mathematical arguments, we show that this difference persists when the range of interaction is assumed to be long (short) ranged with respect to the lattice constant (correlation-length), yielding the critical exponents as given in the original paper.
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