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 language | English |
|---|---|
| Article number | 015208 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 42 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2009 Apr 20 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)
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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 journal › Article
TY - JOUR
T1 - Spanning trees on two-dimensional lattices with more than one type of vertex
AU - Chang, Shu-Chiuan
PY - 2009/4/20
Y1 - 2009/4/20
N2 - 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.
AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=64549158841&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/42/1/015208
DO - 10.1088/1751-8113/42/1/015208
M3 - Article
VL - 42
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 1
M1 - 015208
ER -