Spanning trees on two-dimensional lattices with more than one type of vertex

Shu Chiuan Chang

doi:10.1088/1751-8113/42/1/015208

Spanning trees on two-dimensional lattices with more than one type of vertex

Shu Chiuan Chang

Department of Physics

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

6 Citations (Scopus)

Abstract

For a two-dimensional lattice Λ with n vertices, the number of spanning trees N_ST(Λ) grows asymptotically as exp(nz _Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) z_Λ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z₂₇ = (z_tri + ln 4)/4. Some integral identities are also obtained.

Original language	English
Article number	015208
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	42
Issue number	1
DOIs	https://doi.org/10.1088/1751-8113/42/1/015208
Publication status	Published - 2009

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8113/42/1/015208

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abstract = "For a two-dimensional lattice Λ with n vertices, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) zΛ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z27 = (ztri + ln 4)/4. Some integral identities are also obtained.",

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AB - For a two-dimensional lattice Λ with n vertices, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) zΛ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z27 = (ztri + ln 4)/4. Some integral identities are also obtained.

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Spanning trees on two-dimensional lattices with more than one type of vertex

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