Spanning trees on lattices and integral identities

Shu Chiuan Chang, Wenya Wang

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Article number001
Pages (from-to)10263-10275
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number33
Publication statusPublished - 2006 Aug 18

All Science Journal Classification (ASJC) codes

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


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