Some Exact Results for Spanning Trees on Lattices

Details Some Exact Results for Spanning Trees on Lattices Some Exact Results for Spanning Trees on Lattices

2006-02-24

arxiv.org/abs/cond-mat/0602574v1

J. Phys. A: Math. Gen. 39, 5653-5658 (2006)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 1 table

Scientific paper

10.1088/0305-4470/39/20/001

For $n$-vertex, $d$-dimensional lattices $\Lambda$ with $d \ge 2$, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant $z_{bcc(d)}$ for spanning trees on the $d$-dimensional body-centered cubic lattice. We also give an exact integral expression for $z_{fcc}$ on the face-centered cubic lattice and an exact closed-form expression for $z_{488}$ on the $4 \cdot 8 \cdot 8$ lattice.

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