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	Dimer coverings on random multiple chains of planar honeycomb lattices
	Ren, Haizhen ; Zhang, Fuji ; Qian, Jianguo ; Qian JG(钱建国) ; Zhang FJ(张福基) ; Ren HZ(任海珍)
	2012-08
关键词	dimers (theory) random graphs networks
英文摘要	We study dimer coverings on random multiple chains. A multiple chain is a planar honeycomb lattice constructed by successively fusing copies of a 'straight' condensed hexagonal chain at the bottom of the previous one in two possible ways. A random multiple chain is then generated by admitting the Bernoulli distribution on the two types of fusing, which describes a zeroth-order Markov process. We determine the expectation of the number of the pure dimer coverings (perfect matchings) over the ensemble of random multiple chains by the transfer matrix approach. Our result shows that, with only two exceptions, the average of the logarithm of this expectation (i.e., the annealed entropy per dimer) is asymptotically nonzero when the fusing process goes to infinity and the length of the hexagonal chain is fixed, though it is zero when the fusing process and the length of the hexagonal chain go to infinity simultaneously. Some numerical results are provided to support our conclusion, from which we can see that the asymptotic behavior fits well to the theoretical results. We also apply the transfer matrix approach to the quenched entropy and reveal that the quenched entropy of random multiple chains has a close connection with the well-known Lyapunov exponent of random matrices. Using the theory of Lyapunov exponents we show that, for some random multiple chains, the quenched entropy per dimer is strictly smaller than the annealed one when the fusing process goes to infinity. Finally, we determine the expectation of the free energy per dimer over the ensemble of the random multiple chains in which the three types of dimers in different orientations are distinguished, and specify a series of non-random multiple chains whose free energy per dimer is asymptotically equal to this expectation.; NSFC [10831001, 11061027]
语种	英语
出版者	IOP PUBLISHING LTD
内容类型	期刊论文
源URL	[http://dx.doi.org/10.1088/1742-5468/2012/08/P08002]
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. Dimer coverings on random multiple chains of planar honeycomb lattices[J],2012.
APA	Ren, Haizhen,Zhang, Fuji,Qian, Jianguo,钱建国,张福基,&任海珍.(2012).Dimer coverings on random multiple chains of planar honeycomb lattices..
MLA	Ren, Haizhen,et al."Dimer coverings on random multiple chains of planar honeycomb lattices".(2012).

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