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

Department of Physics

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

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.

Original language	English
Article number	001
Pages (from-to)	10263-10275
Number of pages	13
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	33
DOIs	https://doi.org/10.1088/0305-4470/39/33/001
Publication status	Published - 2006 Aug 18

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/39/33/001

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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

Abstract

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