间约束的定向聚合物的有限尺寸标度函数 吸引墙

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摘要翻译：
本文计算了有限宽度狭缝内通过吸引势与狭缝壁相互作用的有向自避行走的精确解。该模型可以用来模拟聚合物诱导的空间稳定和胶体分散体的敏化絮凝。大宽度渐近导致的相图不同于聚合物附着和吸引在单壁上的相图。由此产生的问题是：一个人能在单壁和两壁情况之间插值吗？本文考虑配分函数同时具有大长度和大宽度的两变量渐近性，计算了配分函数的精确标度函数。因此，我们找到了聚合物在壁面上所引起的力的标度函数。我们发现这些标度函数是由椭圆θ函数给出的。在相图的某些部分，单壁和两壁情况之间有更复杂的交叉，我们解释了这种交叉是如何发生的。
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英文标题：
《Finite-size scaling functions for directed polymers confined between
  attracting walls》
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作者：
A. L. Owczarek, T. Prellberg and A. Rechnitzer
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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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一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
--

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英文摘要：
  The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the polymer-induced steric stabilisation and sensitised floculation of colloidal dispersions. The large width asymptotics led to a phase diagram different to that of a polymer attached to, and attracted to, a single wall. The question that arises is: can one interpolate between the single wall and two wall cases? In this paper we calculate the exact scaling functions for the partition function by considering the two variable asymptotics of the partition function for simultaneous large length and large width. Consequently, we find the scaling functions for the force induced by the polymer on the walls. We find that these scaling functions are given by elliptic theta-functions. In some parts of the phase diagram there is more a complex crossover between the single wall and two wall cases and we elucidate how this happens.
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PDF链接：
https://arxiv.org/pdf/709.3208

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关键词：聚合物 Optimization SIMULTANEOUS asymptotics mathematics 标度 函数 large 敏化 模拟