Spanning Trees on Lattices and Integration Identities

Details Spanning Trees on Lattices and Integration Identities Spanning Trees on Lattices and Integration Identities

2006-04-26

arxiv.org/abs/cond-mat/0604589v1

J. Phys. A: Math. Gen. 39, 10263-10275 (2006)

Physics

Condensed Matter

Statistical Mechanics

15 pages, 3 figures, 1 table

Scientific paper

10.1088/0305-4470/39/33/001

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.

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