Study on dimer models containing impurities

含杂质二聚体模型的研究

• 批准号: 23540155
• 负责人: SADAHIRO Taizo
• 金额: $ 1.08万
• 依托单位: Tsuda College
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540155/
• 关键词: loop erased random walk; hitting matrix; ダイマー模型; 全域木

Perfect matchings on planar bipartite graphs have been extensively studied as the dimer models in statistical mechanics. Almost no results are known for the case in which the underlying graphs are non-bipartite. In this study, we investigate the perfect matchings on the graphs which can be obtained by adding some extra edges tothe planar bipartite graphs, such as square graphs and hexagonal graphs. Extra edges connecting nearest black(or white) vertices. Therefore the perfect matchings on such graphs can be considered as perfect matchings containing impurities in some sence.Generalizing our own results which describes the models with only one, we obtained some results on the cases in which multiple impurities exist. But these results are limited when compared to the single impurity case.

平面二部图上的完美匹配作为统计力学中的二聚体模型得到了广泛的研究。几乎没有结果是已知的情况下，其中的基础图是非二分的。本文研究了平面二部图，如方形图和六角图，通过增加一些额外的边可以得到图的完美匹配。连接最近的黑色（或白色）顶点的额外边。因此，这类图上的完美匹配可以看作是含有某种杂质的完美匹配。推广了我们描述只有一个杂质的模型的结果，得到了关于存在多个杂质的情况的一些结果。但与单一杂质的情况相比，这些结果是有限的。

项目成果

Domino tilings with one diagonal impurity

具有一个对角线杂质的多米诺骨牌

• DOI: 10.3233/fi-2012-699
• 发表时间: 2012
• 期刊: Fund. Inform
• 作者: Nakano;F.;Sadahiro;T
• 通讯作者: T

A (-β)-expansion associated to Sturmian sequences

与 Sturmian 序列相关的 (-β)-扩展

• DOI: 10.1515/integers-2011-0123
• 发表时间: 2012
• 期刊: Integers
• 作者: Nakano;F.;Sadahiro;T
• 通讯作者: T

Hitting Matrix and Domino Tiling with Diagonal Impurities

使用对角线杂质击中矩阵和多米诺骨牌平铺

• 发表时间: 2013
• 期刊: Journal of Statistical Physics
• 影响因子: 1.6
• 作者: T. Hida;Si Si and Win Win Htay,;Si Si;K-S. Lee and Si Si;Si Si;Si Si;Si Si;Si Si;Keisuke Shiromoto;Si Si;石川 喜啓;Si Si;石川喜啓;T. Hida and Si Si;Si Si;渡邉祥, 代田健二;代田健二;F. Nakano T. Sadahiro
• 通讯作者: F. Nakano T. Sadahiro

Domino tilings with diagonal impurities

带有对角杂质的多米诺骨牌瓷砖

• 发表时间: 2009
• 作者: 田原譲;古澤彰浩;杉田聡司;粟木久光;石田学;前田良知;小川美奈;島村宏之;中野史彦
• 通讯作者: 中野史彦