二维聚合物逃逸跃迁的顺序是什么？

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摘要翻译：
当链中单体数目N达到临界值时，端接枝柔性聚合物链在两活塞之间的三维空间中发生由约束线圈向花状构象的突变。在二维几何学中，被限制在有限长2L的条带内的链的单体之间的排除体积相互作用将线圈构象转化为线性的斑点串。然而，斑点图片对这种逃逸过渡的性质提出了问题。为了验证基于斑点图的理论预测，我们用剪枝富集罗森布鲁斯方法(PERM)模拟正方形晶格上的自回避行走，研究了具有排除体积相互作用和一端接枝在长度为2L和宽度为H的条带中间的二维单聚合物链。我们估计了自由能、端到端距离、囚禁单体数、序参量及其分布。结果表明，在大N和大L但有限L/N的热力学极限下，包括序参量在内的几个平均特性有一个小而有限的跃迁。我们还提出了基于Landau自由能方法的理论描述，与模拟结果吻合良好。模拟结果和解析理论都表明二维逃逸跃迁是一种弱一级相变。
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英文标题：
《What is the order of 2D polymer escape transition?》
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作者：
Hsiao-Ping Hsu, Kurt Binder, Leonid I. Klushin, and Alexander M.
  Skvortsov
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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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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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英文摘要：
  An end-grafted flexible polymer chain in 3d space between two pistons undergoes an abrupt transition from a confined coil to a flower-like conformation when the number of monomers in the chain, N, reaches a critical value. In 2d geometry, excluded volume interactions between monomers of a chain confined inside a strip of finite length 2L transform the coil conformation into a linear string of blobs. However, the blob picture raises questions on the nature of this escape transition. To check the theoretical predictions based on the blob picture we study 2d single polymer chains with excluded volume interactions and with one end grafted in the middle of a strip of length   2L and width H by simulating self-avoiding walks on a square lattice with the pruned-enriched-Rosenbluth method (PERM). We estimate the free energy, the end-to-end distance, the number of imprisoned monomers, the order parameter, and its distribution. It is shown that in the thermodynamic limit of large N and L but finite L/N, there is a small but finite jump in several average characteristics, including the order parameter. We also present a theoretical description based on the Landau free energy approach, which is in good agreement with the simulation results. Both simulation results and the analytical theory indicate that the 2d escape transition is a weak first-order phase transition.
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PDF链接：
https://arxiv.org/pdf/704.1857

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关键词：聚合物 interactions distribution interaction Theoretical 具有 研究 order 提出