摘要翻译：
本文利用平均球面近似(MSA)和Percus-Yevick(PY)积分方程理论，计算了具有长程各向异性相互作用的球形粒子模型在向列相中的对关联函数。MSA理论的结果与Holovko和Sokolovska(J.Mol.Liq.$\bf 82,161（1999））的分析结果进行了比较。利用一个包含对称守恒部分和对称破缺部分的自由能泛函研究了向列相的性质。我们还研究了用直接对关联函数构造一个自由能泛函的可能性，该泛函只包含有序相的主序参量，得到的泛函结果与原泛函一致。用大热力学势对各向同性向列相转变进行了定位。PY理论给出了具有对相关函数的向列相，谐波系数具有所需的所有特征。在向列相中，与指向矢横向涨落关联有关的总对关联函数$h({bf x_1},{bf x_2}）的调和系数应发展为长程尾。在MSA和PY理论中都发现了这一特征。
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英文标题：
《Pair Correlation Functions and a Free-Energy Functional for the Nematic
  Phase》
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作者：
Pankaj Mishra, Swarn Lata Singh, Jokhan Ram and Yashwant Singh
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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：
  In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation(MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska (J. Mol. Liq. $\bf 82$, 161(1999)). A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function $h({\bf x_1},{\bf x_2})$ connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories.
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PDF链接：
https://arxiv.org/pdf/706.0067