On the entropy of spanning trees on a large triangular lattice
Statistical Mechanics
2007-05-23 v2 Combinatorics
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} 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} - ...)
Keywords
Cite
@article{arxiv.cond-mat/0309198,
title = {On the entropy of spanning trees on a large triangular lattice},
author = {M. L. Glasser and F. Y. Wu},
journal= {arXiv preprint arXiv:cond-mat/0309198},
year = {2007}
}
Comments
16 pages, 3 figures, reference added, for Proceedings of the Gainesville Conference on Number Theory and Combinatorics in Physics, Ramanujan Journal