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 |
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Article number | 015208 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 42 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2009 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)