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Spanning Trees on Lattices and Integration Identities

Shu-Chiuan Chang·Wenya Wang
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Abstract

For a lattice $Λ$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(Λ)$ grows asymptotically as $\exp(n z_Λ)$ 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 integration 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.

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Shu-Chiuan Chang, Wenya Wang. 2006-04-26. Spanning Trees on Lattices and Integration Identities. https://doi.org/10.1088/0305-4470%2F39%2F33%2F001

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