On the entropy of spanning trees on a large triangular lattice

Details On the entropy of spanning trees on a large triangular lattice On the entropy of spanning trees on a large triangular lattice

2003-09-08

arxiv.org/abs/cond-mat/0309198v2

Ramanujian J. 10, 205-214 (2005).

Physics

Condensed Matter

Statistical Mechanics

16 pages, 3 figures, reference added, for Proceedings of the Gainesville Conference on Number Theory and Combinatorics in Phys

Scientific paper

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} d\theta \int_0^{2 Pi} 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} - ...)

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