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

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 μ = 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 asanoba lattice at n = 1.