1202.5623 (Chengxiang Ding et al.)

Exact critical points of the O($n$) loop model on the martini and the
3-12 lattices    [PDF]

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