The O(n) loop model on the 3-12 lattice

Abstract

The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3-12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related via a simple transformation of variables. When n=0 this gives the recently found exact value $\mu =\mathrm{1.711041...}$ for the connective constant of self-avoiding walks on the 3-12 lattice. The exact critical points are recovered for the Ising model on the 3-12 lattice and the dual asanoha lattice at n=1.

7 pages, 3 eps figs

References in corpus (2)

• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Exact Results for the Adsorption of a Flexible Self-Avoiding Polymer Chain in Two Dimensions

Cited by in corpus (2)

• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Exact critical points of the O($n$) loop model on the martini and the 3-12 lattices