Some exact results for spanning trees on lattices

Shu Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant zbcc(d) for spanning trees on the d-dimensional body-centred cubic lattice. We also give an exact integral expression for zfcc on the face-centred cubic lattice and an exact closed-form expression for z488 on the 4 8 8 lattice.

Original languageEnglish
Pages (from-to)5653-5658
Number of pages6
JournalJournal of Physics A: Mathematical and General
Volume39
Issue number20
DOIs
Publication statusPublished - 2006 May 19

All Science Journal Classification (ASJC) codes

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

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