Spanning trees on lattices and integral identities

Shu Chiuan Chang; Wenya Wang

doi:10.1088/0305-4470/39/33/001

Spanning trees on lattices and integral identities

Shu Chiuan Chang, Wenya Wang

物理學系

研究成果: Article › 同行評審

22 引文斯高帕斯（Scopus）

摘要

For a lattice Λ with n vertices and dimension d equal to or higher than 2, the number of spanning trees N_ST(Λ) increases asymptotically as exp(nz_Λ) in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant z _Λ for spanning trees on several lattices. By taking different unit cells in the calculation, many integral identities can be obtained. We also give z_Λ(p) on the homeomorphic expansion of k-regular lattices with p vertices inserted on each edge.

原文	English
文章編號	001
頁（從 - 到）	10263-10275
頁數	13
期刊	Journal of Physics A: Mathematical and General
卷	39
發行號	33
DOIs	https://doi.org/10.1088/0305-4470/39/33/001
出版狀態	Published - 2006 8月 18

All Science Journal Classification (ASJC) codes

統計與非線性物理學
數學物理學
一般物理與天文學

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AB - For a lattice Λ with n vertices and dimension d equal to or higher than 2, the number of spanning trees NST(Λ) increases asymptotically as exp(nzΛ) in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant z Λ for spanning trees on several lattices. By taking different unit cells in the calculation, many integral identities can be obtained. We also give zΛ(p) on the homeomorphic expansion of k-regular lattices with p vertices inserted on each edge.

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Spanning trees on lattices and integral identities

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