摘要翻译：
试图用粗粒分子理论来计算聚合物混合物关联的随机相近似(RPA)的修正，一直受到对任意截止长度值的不必要的敏感性的困扰，{\\即}，由于紫外(UV)发散。我们分析了反结构因子$S^{-1}(k)$的紫外发散度，用类似于以前几个研究中所用的一个“环”近似进行了预测。我们既考虑了可混溶的均聚物共混物，也考虑了无序的二嵌段共聚物熔体。我们证明，在这两种情况下，所有的紫外发散贡献都可以吸收到广义自洽场论(SCFT)的唯象参数值的重整化中。这一观察允许构造一个对SCFT现象学修正的紫外收敛理论。UV发散单环对$s^{-1}(k)$的贡献显示为：(i)$k$独立的贡献，由有效的$chi$参数的重整化引起；(ii)由单体统计链段长度的重整化引起的$k$相关的贡献；(iii)由单环涨落自由能的平方梯度贡献引起的与$k^{2}$成正比的贡献；(iv)$k$相关的贡献，与聚合度成反比的贡献，由嵌段共聚物链端附近和嵌段连接附近流体结构的局部扰动引起。
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英文标题：
《Renormalization of the one-loop theory of fluctuations in polymer blends
  and diblock copolymer melts》
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作者：
Piotr Grzywacz, Jian Qin, and David C. Morse
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, {\it i.e.}, by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor $S^{-1}(k)$ predicted by a `one-loop' approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of a UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to $S^{-1}(k)$ are shown to be the sum of: (i) a $k$-independent contribution that arises from a renormalization of the effective $\chi$ parameter, (ii) a $k$-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to $k^{2}$ that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a $k$-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.
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PDF链接：
https://arxiv.org/pdf/710.551