Spanning trees on two-dimensional lattices with more than one type of vertex

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For a two-dimensional lattice Λ with n vertices, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) zΛ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z27 = (ztri + ln 4)/4. Some integral identities are also obtained.

Original languageEnglish
Article number015208
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number1
DOIs
Publication statusPublished - 2009 Apr 20

Fingerprint

Spanning tree
apexes
Entropy
entropy
Vertex of a graph
Thermodynamic Limit
triangles
Triangle
Closed-form
Thermodynamics
thermodynamics

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

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abstract = "For a two-dimensional lattice Λ with n vertices, the number of spanning trees NST(Λ) grows asymptotically as exp(nz Λ) in the thermodynamic limit. We present an exact integral expression and a numerical value for the entropy (asymptotic growth constant) zΛ for spanning trees on 19 two-dimensional lattices with more than one type of vertex given in O'Keeffe and Hyde (1980 Philos. Trans. R. Soc. A 295 553). Especially, an exact closed-form expression for the entropy is derived for net 14, and the entropies of net 27 and the triangle lattice have the simple relation z27 = (ztri + ln 4)/4. Some integral identities are also obtained.",
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Spanning trees on two-dimensional lattices with more than one type of vertex. / Chang, Shu-Chiuan.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 1, 015208, 20.04.2009.

Research output: Contribution to journalArticle

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