title: Critical points of the O(n) loop model on the martini and the 3-12 lattices.
abstract: We derive the critical line of the O(n) loop model on the martini lattice as a function of the loop weight n basing on the critical points on the honeycomb lattice conjectured by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. In the limit n→0 we prove the connective constant μ=1.7505645579⋯ of self-avoiding walks on the martini lattice. A finite-size scaling analysis based on transfer matrix calculations is also performed. The numerical results coincide with the theoretical predictions with a very high accuracy. Using similar numerical methods, we also study the O(n) loop model on the 3-12 lattice. We obtain similarly precise agreement with the critical points given by Batchelor [J. Stat. Phys. 92, 1203 (1998)].
authors.affiliation: Physics Department, Anhui University of Technology, Maanshan 243002, People's Republic of China.
authors.forename: Chengxiang
authors.initials: C
authors.lastname: Ding
authors.forename: Zhe
authors.initials: Z
authors.lastname: Fu
authors.forename: Wenan
authors.initials: W
authors.lastname: Guo
mesh_terms: D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular