用基体永久近似单体-二聚体常数

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摘要翻译：
单体-二聚体模型是统计力学的基础。然而，它在计算上是$#p$-完全的，即使对于二维问题也是如此。本文通过将二部图的全部匹配数转化为扩展二部图的完全匹配数，给出了单体-二聚体模型配分函数的矩阵永久表达式。采用序贯重要性抽样算法计算永久物。对于具有周期条件的二维晶格，我们得到了$0.6627\PM0.0002$,精确值为$H2=0.662798972834$。对于具有周期条件的三维晶格，我们的数值结果是$0.7847\pM0.0014$,{符合已知的界$0.7653\leqH_3\leq0.7862$
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英文标题：
《Approximating the monomer-dimer constants through matrix permanent》
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作者：
Yan Huo, Heng Liang, Si-Qi Liu, Fengshan Bai
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最新提交年份：
2007
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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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英文摘要：
  The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model 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, we obtain $ 0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $ 0.7847\pm0.0014$, {which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.}
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PDF链接：
https://arxiv.org/pdf/708.1641

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关键词：Transforming Dimensional Statistical Fundamental Computation dimensional 具有 lattice two matchings