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	Computing monomer-dimer systems through matrix permanent
	Yan Huo ; Heng Liang ; Si-Qi Liu ; Fengshan Bai
	2010-10-12 ; 2010-10-12
关键词	Theoretical or Mathematical/ importance sampling lattice theory matrix algebra numerical analysis statistical mechanics/ monomer-dimer systems matrix permanent statistical mechanics partition function bipartite graph sequential importance sampling algorithm two-dimensional lattice robustness numerical analysis/ A0520 Statistical mechanics A0250 Probability theory, stochastic processes, and statistics A0550 Lattice theory and statistics Ising problems A0270 Computational techniques A0210 Algebra, set theory, and graph theory
中文摘要	The monomer-dimer model is fundamental in statistical mechanics. However, it is #P-complete in computation, even for two-dimensional problems. A formulation for the partition function of the monomer-dimer system is proposed in this paper by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, the monomer-dimer constant is known as h/sub 2/=0.662798972834. We obtain 0.6627+/-0.0002 for our approximation, which shows the robustness and the efficiency of the algorithm. For three-dimensional problem, our numerical result is 0.7847+/-0.0014, which agrees with the best known bounds.
语种	英语
出版者	American Physical Society ; USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81235]
专题	清华大学
推荐引用方式 GB/T 7714	Yan Huo,Heng Liang,Si-Qi Liu,et al. Computing monomer-dimer systems through matrix permanent[J],2010, 2010.
APA	Yan Huo,Heng Liang,Si-Qi Liu,&Fengshan Bai.(2010).Computing monomer-dimer systems through matrix permanent..
MLA	Yan Huo,et al."Computing monomer-dimer systems through matrix permanent".(2010).

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