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On the entropy of spanning trees on a large triangular lattice

M. L. Glasser·F. Y. Wu
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Abstract

The double integral representing the entropy S_{tri} 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 S_{tri} = [1/(2 Pi)]^2 \int_0^{2 Pi} dθ\int_0^{2 Pi} dϕln [6-2 cos(θ) - 2 cos(ϕ) -2 cos(θ+ϕ)] = [3(\sqrt 3)/Pi](1 - 5^{-2} + 7^{-2} - 11^{-2} + 13^{-2} - ...)

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M. L. Glasser, F. Y. Wu. 2003-09-11. On the entropy of spanning trees on a large triangular lattice. https://arxiv.org/abs/cond-mat/0309198

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