准直硬质流体的基测度密度泛函 六边形：基本测度理论的新见解

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摘要翻译：
本文得到了平面上对齐硬六边形模型的一个基本测度泛函。我们的目的不仅仅是为一个新的，诚然是学术的模型提供一个功能，而是调查基本测量理论的结构。对齐硬六边形的模型与硬盘模型有相似之处。两者都有“丢失的情况”，即承认三个粒子的构型，其中存在成对重叠但不存在三重重叠。已知这些配置对于基本度量功能是有问题的，它们不能正确地捕获它们的贡献。这种失败在于这些函数不能给出正确的三阶直接相关函数的低密度极限。这里我们通过在平面x+y+z=0上投影对齐的硬立方体来导出泛函。这些函数的正确的维交叉行为允许我们遵循这个策略。然而，对齐硬立方体的泛函没有丢失的情况，因此对齐硬六边形的结果泛函也没有丢失。事实上，与硬盘相比，后者表现出一种特殊的结构。它依赖于一个加权密度的单参数族，通过一个新的术语没有出现在硬盘的函数中。除了研究这个系统的冻结，我们还讨论了功能结构对基本测度理论新发展的影响。
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英文标题：
《Fundamental-measure density functional for the fluid of aligned hard
  hexagons: New insights in fundamental measure theory》
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作者：
Jose A. Capitan and Jose A. Cuesta
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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 article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share "lost cases", i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane x+y+z=0. The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through a new term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for new developments of fundamental measure theory.
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PDF链接：
https://arxiv.org/pdf/704.2379

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关键词：六边形 新见解 Implications Developments Similarities 对齐 measure 泛函 遵循 new