On the Entropy of Spanning Trees on a Large Triangular Lattice |
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| Authors: | M.?L.?Glasser mailto:lglasser@twcny.rr.com" title=" lglasser@twcny.rr.com" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,F.?Y.?Wu |
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| Affiliation: | (1) Department of Physics, Clarkson University, Potsdam, New York, 13699;(2) Department of Physics, Northeastern University, Boston, Massachusetts, 02115 |
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| Abstract: | ![]()
The double integral representing the entropy Stri of spanning trees on a large triangular lattice is evaluated using two different methods, one algebraic and one graphical. Both methods lead to the same result 2000 Mathematics Subject Classification: Primary—05A16, 33B30, 82B20 |
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| Keywords: | triangular lattice spanning tree dilogarithm |
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![$$ S_{rm tri} = (4 pi^2)^{-1} int_{0}^{2 pi} d theta int^{2 pi}_{0}d phi ln {[}6-2 cos theta-2 cos phi-2 cos (theta + phi){]} = (3 sqrt{3}/pi)(1-5^{-2} + 7^{-2} - 11^{-2} + 13^{-2}-ldots).$$](/content/fn900700677516u7/11139_2005_Article_4847_TeX2GIFEqu1.gif)