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摘要翻译：
在最近的一篇论文[F.Wang和F.Y.Wu,Phys.Rev.E75(2007)040105(R)]中，我们报道了无限kagome晶格上密排二聚体的精确计数结果。我们用Pfaffian方法和顶点模型公式计算了每个二聚体的自由能，得到了一个简单的表达式。我们还报告了关于二聚体-二聚体相关性的结果，但没有给出细节。本文详细介绍了相关函数分析。此外，我们还将精确枚举推广到两种不同边界条件下的有限格，并且具有非对称二聚体权值。对于对称的二聚体权重，有限格的结果同样是简单的，我们证明它们可以用自旋变量映射来理解。我们还描述了Grassmanian泛函积分方法的形式，并将其应用于kagome格。
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英文标题：
《Close-packed dimers on the kagome lattice: Finite lattices and the
Grassmannian approach》
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作者：
Fa Wang, F. Y. Wu
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最新提交年份：
2008
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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：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：
In a recent paper [ F. Wang and F. Y. Wu, Phys. Rev. E 75 (2007) 040105(R) ] we reported exact results on the enumeration of close-packed dimers on an infinite kagome lattice. We computed the per-dimer free energy using both the Pfaffian approach and a vertex-model formulation, and found the result given by a simple expression. We also reported results on dimer-dimer correlations without giving details. In this paper we present details of the correlation function analysis. In addition, we extend the exact enumeration to finite lattices under two different boundary conditions and with asymmetric dimer weights. For symmetric dimer weights the finite-lattice results are again simple, and we show that they can be understood using a spin variable mapping. We also describe the formulation of a Grassmannian functional integral approach and apply it to the kagome lattice.
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PDF链接：
https://arxiv.org/pdf/711.4788
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