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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