2013 Fiscal Year Final Research Report
Study on dimer models containing impurities
| Project/Area Number |
23540155
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tsuda College |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | loop erased random walk |
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| Research Abstract |
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 to
the 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.
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