摘要翻译：
我们研究了位于三维Sierpinski垫片(3DSG)的分形容器中的由两个聚合物链组成的聚合物体系。每个三维SG分形有四个分形不可穿透的二维曲面，它们实际上是二维SG分形。双聚合物体系是由两个相互作用的自回避行走（锯）模拟的，其中一个代表三维漂浮的聚合物，而另一个对应于粘附在四个二维SG边界之一上的链。我们假设所研究的体系浸没在一种较差的溶剂中，诱导了链内相互作用。对于链间的相互作用，我们提出了两个模型：第一个模型(ASAWs)中的SAW链是相互回避的，而第二个模型(CSAWs)中的SAW链是相互交叉的。应用精确重整化群(RG)方法，建立了具有避免锯的三维SG分形族中$B=2,3$和$B=4$分形的相图，以及具有交叉锯的三维SG分形族中$B=2和$B=3$分形的相图。同时，在适当的过渡不动点处，我们计算了接触临界指数，它与不同链的单体之间的接触数有关。在整个论文中，我们比较了两个模型的结果，并讨论了底层晶格的拓扑结构对出现相图的影响。
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英文标题：
《Critical behavior of interacting two-polymer system in a fractal
  solvent: an exact renormalization group approach》
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作者：
Ivan Zivic, Suncica Elezovic-Hadzic and Sava Milosevic
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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：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：
  We study the polymer system consisting of two polymer chains situated in a fractal container that belongs to the three--dimensional Sierpinski Gasket (3D SG) family of fractals. Each 3D SG fractal has four fractal impenetrable 2D surfaces, which are, in fact, 2D SG fractals. The two-polymer system is modelled by two interacting self-avoiding walks (SAWs), one of them representing a 3D floating polymer, while the other corresponds to a chain adhered to one of the four 2D SG boundaries. We assume that the studied system is immersed in a poor solvent inducing the intra-chain interactions. For the inter-chain interactions we propose two models: in the first model (ASAWs) the SAW chains are mutually avoiding, whereas in the second model (CSAWs) chains can cross each other. By applying an exact Renormalization Group (RG) method, we establish the relevant phase diagrams for $b=2,3$ and $b=4$ members of the 3D SG fractal family for the model with avoiding SAWs, and for $b=2$ and $b=3$ fractals for the model with crossing SAWs. Also, at the appropriate transition fixed points we calculate the contact critical exponents, associated with the number of contacts between monomers of different chains. Throughout the paper we compare results obtained for the two models and discuss the impact of the topology of the underlying lattices on emerging phase diagrams.
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PDF链接：
https://arxiv.org/pdf/712.2941