Monomer-dimer problem on random planar honeycomb lattice

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	Monomer-dimer problem on random planar honeycomb lattice
	Ren, Haizhen ; Zhang, Fuji ; Qian, Jianguo ; Qian JG(钱建国)
刊名	http://dx.doi.org/10.1063/1.4866317
	2014
关键词	STATISTICAL-MECHANICS LYAPUNOV EXPONENTS PERMANENT MATRICES ENTROPY SYSTEMS NUMBER MODEL
英文摘要	National Natural Science Foundation of China [11271307, 11061027]; We consider the monomer-dimer (MD) problem on a random planar honeycomb lattice model, namely, the random multiple chain. This is a lattice system with non-periodic boundary condition, whose generating process is inspired by the growth of single walled zigzag carbon nanotubes. By applying algebraic and combinatorial techniques we establish a calculating expression of the MD partition function for bipartite graphs, which corresponds to the permanent of a matrix. Further, by using the transfer matrix argument we show that the computing problem of the permanent of high order matrix can be converted into some lower order matrices for this family of lattices, based on which we derive an explicit recurrence formula for evaluating the MD partition function of multiple chains and random multiple chains. Finally, we analyze the expectation of the number of monomer-dimer arrangements on a random multiple chain and the asymptotic behavior of the annealed MD entropy when the multiple chain becomes infinite in width and length, respectively. (C) 2014 AIP Publishing LLC.
语种	英语
出版者	AMER INST PHYSICS
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91370]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Ren, Haizhen,Zhang, Fuji,Qian, Jianguo,et al. Monomer-dimer problem on random planar honeycomb lattice[J]. http://dx.doi.org/10.1063/1.4866317,2014.
APA	Ren, Haizhen,Zhang, Fuji,Qian, Jianguo,&钱建国.(2014).Monomer-dimer problem on random planar honeycomb lattice.http://dx.doi.org/10.1063/1.4866317.
MLA	Ren, Haizhen,et al."Monomer-dimer problem on random planar honeycomb lattice".http://dx.doi.org/10.1063/1.4866317 (2014).