Tuesday, February 28, 2012

1202.5623 (Chengxiang Ding et al.)

Exact critical points of the O($n$) loop model on the martini and the
3-12 lattices
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Chengxiang Ding, Zhe Fu, Wenan Guo
We derive the exact critical points of the O($n$) loop model on the martini lattice as a function of $n$. The result is verified by a finite-size scaling analysis based on transfer matrix calculations.The numerical results coincide with the theoretical predictions with an accuracy up to 9 decimal numbers. At the limit $n\to 0$, this gives the exact connective constant $\mu=1.7505645579...$ of self-avoiding walks on the martini lattice, which is obtained for the first time to our knowledge. The exact critical points of the O($n$) loop model on the 3-12 lattice obtained by Batchelor [J. Stat. Phys. {\bf 92}, 1203(1998)] are also verified.
View original: http://arxiv.org/abs/1202.5623

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