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arXiv 1004.1698cond-mat.stat-mech
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狭缝中场与壁相互作用离散(1+1)维RSOS模型的精确解

Exact Solution of the Discrete (1+1)-dimensional RSOS Model in a Slit with Field and Wall Interactions

Aleksander L Owczarek, Thomas Prellberg

摘要:

本文给出了一个被限制在狭缝中的线性限制性固体叠固体(RSOS)模型的解。我们包括一个类似场的能量,相当于加权的界面下的面积,也包括独立的相互作用条款与两个墙壁。这个模型也可以映射到一个晶格聚合物模型的Motzkin路径在一个狭缝与两个墙壁相互作用,并包括渗透压。这项工作概括了以前的工作RSOS模型的半平面,最近被证明表现出一种新的数学结构,涉及基本的超几何函数${}_3ϕ_2$的解决方案。由于半平面和狭缝之间的数学关系,因此这项工作有效地探索了潜在的$q$ -正交多项式结构的解决方案。它还概括了其他两个最近的作品:一个戴克路径加权渗透压在狭缝和另一个有关Motzkin路径没有渗透压项在狭缝。

英文摘要:

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model confined to a slit. We include a field-like energy, which equivalently weights the area under the interface, and also include independent interaction terms with both walls. This model can also be mapped to a lattice polymer model of Motzkin paths in a slit interacting with both walls and including an osmotic pressure. This work generalises previous work on the RSOS model in the half-plane which has a solution that was shown recently to exhibit a novel mathematical structure involving basic hypergeometric functions ${}_3ϕ_2$. Because of the mathematical relationship between half-plane and slit this work hence effectively explores the underlying $q$-orthogonal polynomial structure to that solution. It also generalises two other recent works: one on Dyck paths weighted with an osmotic pressure in a slit and another concerning Motzkin paths without an osmotic pressure term in a slit.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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